Determination of light absorption pathlength in a vertical-beam photometer

ABSTRACT

Disclosed are photometric methods and devices for determining optical pathlength of liquid samples containing analytes dissolved or suspended in a solvent. The methods and devices rely on determining a relationship between the light absorption properties of the solvent and the optical pathlength of liquid samples containing the solvent. This relationship is used to establish the optical pathlength for samples containing an unknown concentration of analyte but having similar solvent composition. Further disclosed are methods and devices for determining the concentration of analyte in such samples where both the optical pathlength and the concentration of analyte are unknown. The methods and devices rely on separately determining, at different wavelengths of light, light absorption by the solvent and light absorption by the analyte. Light absorption by the analyte, together with the optical pathlength so determined, is used to calculate the concentration of the analyte. Devices for carrying out the methods particularly advantageously include vertical-beam photometers containing samples disposed within the wells of multi-assay plates, wherein the photometer is able to monitor light absorption of each sample at multiple wavelengths, including in the visible or UV-visible region of the spectrum, as well as in the near-infrared region of the electromagnetic spectrum. Novel photometer devices are described which automatically determine the concentration of analytes in such multi-assay plates directly without employing a standard curve.

This is a Divisional of prior application Ser. No. 09/220,177 filed Dec.23, 1998.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to the field of photometry. In particular, theinvention relates to spectrophotometric methods and apparatus capable ofdetermining the light absorption pathlength for various samples to beanalyzed with a spectrophotometer.

2. Description of the Related Art

The problem of an undefined light absorption pathlength in vertical-beamphotometers has existed since the advent of vertical-beam photometers,i.e., for over 20 years. Substantial errors in determination byvertical-beam photometry of either relative optical pathlength or theconcentration of analytes in a solvent contained in a sample-retainingdevice of unknown optical pathlength by prior art methods occur becauseof 1) substantial variation in solvent temperature, 2) substantialvariation in the solvent composition, 3) substantial presence ofmaterials in the samples which absorb light in the wavelength regionwhere the optical pathlength of the solvent is being monitored and 4)optical aberrations which occur upon passing analysis light though thevariable curved meniscus of samples having a liquid-gas interface.

Photometry is a common measurement technique employed to monitor opticalcharacteristics of samples. Customarily, samples contain an analytespecies dissolved in a solvent at an unknown concentration. Theconcentration of the analyte in a sample may be determined by using aphotometric device to measure the fraction of light absorbed by thesample at a specific wavelength (λ). The value of λ is usually chosen tobe near the wavelength of light where the analyte absorbs maximally.According to the Beer-Lambert law, equation 1, absorbance is determinedas follows: $\begin{matrix}{{{Absorbance}\quad \left( A_{\lambda} \right)} = {{\log \quad \frac{I_{o}}{I}} = {ɛ_{\lambda} \cdot l \cdot C}}} & (1)\end{matrix}$

where I_(O) is the incident radiation intensity, I is the intensity oflight emerging from the sample, ε_(λ) is the molar extinctioncoefficient of the analyte dissolved in the solvent, is the lightabsorption pathlength, and C is the concentration of absorbing analytein the solvent. The value of I customarily is measured with aphotometric apparatus, such as a photometer or spectrophotometer,equipped with a fixed light path sample-retaining device called acuvette, such as a 1 cm light absorption pathlength cuvette. Thesample-retaining device contains a sample comprised of analyte dissolvedin a solvent. The value of I_(O) is ordinarily measured with the samesystem (photometric apparatus, sample-retaining device and solventexcept that no analyte is present in the solvent. Alternatively, I_(O)may be measured in the absence of both the sample and thesample-retaining device (this value of I_(O) is called an “air blank”).When an “air blank” is employed, a separate A_(λ) measurement of thesolvent and sample-retaining device gives a “solvent blank” absorbancevalue. A “corrected absorbance” value related to absorbance of theanalyte is then obtained by subtracting the “solvent blank” from eachabsorbance measurement made on the samples comprised of analytedissolved in solvent and contained in the sample-retaining device. Thesetwo alternative procedures and combinations thereof give mathematicallyequivalent results. Absorbance measurements made by either procedureallows unknown concentrations of the analyte to be determined bycalculation according to Eq. 1, provided that ελ and l are known.

A spectrophotometer is a photometric apparatus which employs anadjustable means to pre-select a desired portion of the electromagneticspectrum as incident radiation. Usually spectrophotometers employ amonochrometer having a dispersive means, such as a prism ordiffraction-grating, to provide continuously selectable, narrow, bandsof light centered about the desired wavelength λ. Most conventionalphotometers and spectrophotometers employ a horizontal light beam thattraverses the liquid sample so as to avoid passing through a liquid-gasinterface that is typically above the sample. With such horizontal-beamphotometers, the geometry and optical pathlength within the sample isfixed for any given cuvette. Cuvettes for visible and ultraviolet lightabsorption measurements customarily have a 1 cm pathlength. Cuvetteswith pathlengths between 0.1 cm and 10 cm are also common, however. Withany such fixed pathlength cuvette in a horizontal-beam photometers,unknown concentrations C of the analytes may be calculated fromabsorbance measurements provided that the values of ε_(λ) and l areknown.

When either ε_(λ) and l is not known, values of C may be determinedreadily by employing known concentrations of the analyte dissolved inthe same solvent (i.e., “standards”) and performing similarlight-absorbance measurements on unknown concentrations of analytedissolved in the same solvent and on the standards. The most commonprocedure comprises plotting A_(λ) versus concentration of analyte inthe standards (i.e., a “standard curve”) and then comparing the resultsobtained with the unknown concentrations of analyte to the standardcurve. This procedure allows determination of the unknown concentrationsof analyte from the “standard curve”.

Vertical-beam photometers also measure light absorption in order todetermine the unknown concentrations of analyte in samples. Invertical-beam, photometers, however, the light beam usually passes onlythrough one wall of the sample-retaining device, through the sample, andthen through the interface between the sample a surrounding gasatmosphere (which is usually air). The latter liquid-gas interface, themeniscus, is usually curved, the specific shape depending upon theinteractions between the liquid sample and the gas and the side-walls ofthe sample retaining device. Depending upon the design of a particularvertical-beam photometer, the light beam may traverse the meniscuseither before or after passing through the sample. In either case, theoptical pathlength through the sample is not a constant value. Instead,the optical pathlength is related to the sample volume and the meniscusshape. The nature of the sample, the sample-retaining device surfaces,and gas each contributes to the shape of the meniscus, quantitativelyaffecting the optical pathlength through the sample. Thus, in verticalbeam photometers, the value of l in Eq. 1 usually is unknown and isdifficult to control reproducibly.

Vertical-beam photometry has become a popular technique despite thedisadvantage of not having a fixed optical pathlength through thesample. This popularity stems from the fact that the opticalcharacteristics of a large multiplicity of samples may be analyzed witha vertical-beam photometer in a small period of time. Typically,vertical-beam photometers monitor the optical characteristics of samplesdisposed in the wells of, for example, 96 well multi-assay plates. Theoptical characteristics, such as light absorption or light scattering,of the samples contained within each well of such multi-assay plates maybe monitored, typically, in 10 seconds or less, and generally in oneminute or less. Vertical-beam photometers also allow repetitivemeasurements of such a multiplicity of samples to be made typically withintervals of 10 seconds or less (and generally in one minute or less)between each of a series of measurements. In such a way the kineticproperties, such as the rate of change in absorbance, of a plurality ofsamples may be monitored in a very short time.

In vertical-beam photometry of the prior art, an approximated constantvalue of l is used for standards and unknowns. Concentrations of unknownanalytes are determined, often with acceptable precision, by plotting“standard curves” using the approximated value of l and comparing theabsorbance results obtained with unknown concentrations of analyte tothe standard curve, as mentioned previously.

The fact that a value of C may not be calculated directly from Eq. 1,but instead must be determined from a standard curve constructed foreach analytical measurement, severely hinders the ability ofvertical-beam photometric techniques. The additional time and expenserequired for preparing such standard curves for each analysis is oftenan onerous disadvantage to vertical-beam photometry. Thus, convenient,accurate, and precise methods and apparatus for determining opticalpathlength of samples in vertical-beam photometers would be of greatutility.

Japanese Kokai Patent Application number Sho58[1983]-1679Y2 disclosesthat the unknown optical pathlength of vessels may be determined bydispensing a colored solution, with a known relationship between opticalpathlength and color absorbance, into the vessels and determining thecolor absorbance of this solution. A similar method is taught in U.S.Pat. No. 5,298,978, issued Mar. 29, 1994.

Additionally Japanese Kokai Patent Application numbers Sho60(1985]-183560 and Sho 61[1986]-82145 disclose methods of determiningrelative optical pathlength of aqueous samples within different reactorvessels (contained in a common reactor) by measuring the optical densityof the samples at two different wavelengths in the near-infraredwavelength region from 900 to 2100 nanometers. With clear quartzreaction vessels, the reference teaches that (A₉₇₅−A₉₀₀), (A₁₁₉₅−A₁₀₇₀),or (A₁₂₆₀−A₁₀₇₀) may be used to determine the relative opticalpathlength through aqueous samples. For reactors made of synthetic acrylresins, where the resin has interfering absorption bands, the prior artteaches that (A₉₇₀−A₁₀₇₀) or (A₁₂₈₀−A₁₀₇₀) may be used to determinerelative optical pathlength of the samples. Once relative opticalpathlength is known for each of the vessels of the reactor, then opticaldensity values of analyte (measured at a third wavelength) may benormalized for variation in optical pathlength to obtain the relativeconcentration of analyte in each reactor vessel. Employing vessels withknown concentrations of analyte allows one to determine the absoluteconcentrations of analyte within other vessels.

There also exists need for methods and apparatus that may be utilizedwith samples that are dissolved in a variety of different solvents or inmixtures of different solvents. Because analytes are extremely diverseand may have diverse light-absorption properties, there exists noapparatus capable of determining concentration and optical pathlength ofany analyte dissolved in various solvents or mixtures of solvents.Further complicating this situation is the extreme variability ofconcentrations of analytes from one sample to the next.

SUMMARY OF THE INVENTION

The instant invention provides a solution to the problem of undefinedlight absorbance pathlength in vertical-beam photometers. The inventionprovides methods and devices that are convenient to employ and thatrequire minimal additional measurement apparatus. Thus, the costassociated with making such measurement is kept to a minimum.

The invention further provides methods and apparatus for determiningoptical pathlength and sample concentration that furnish accurate andreproducible results. The results, determined by using the invention invertical-beam photometers, are essentially interchangeable andindistinguishable from those obtained in horizontal-beam photometry.

The invention also provides methods and apparatus for determiningoptical pathlengths between 1 millimeter and 1 centimeter in aqueoussamples within vertical-beam photometers. The inventive methods andapparatus may be utilized with samples that are dissolved in a varietyof different solvents or in mixtures of different solvents.

Thus, in one embodiment of the invention, optical pathlength isdetermined in vertical-beam photometers by analyzing an optical propertyof the sample solvent which is dependent upon optical pathlength butindependent of all relevant concentrations of all analytes which maypossibly be contained within a sample solvent.

In one aspect, the invention provides multi-channel photometric analysisdevices for determining optical characteristics of analytes in sets ofliquid-containing samples having unknown optical pathlengths. Thesedevices comprise

a. a first sample holder for holding the sets of liquid-containingsamples in one or more substantially vertical optical channels;

b. a means for positioning the sets of samples in the optical channels;

c. a light source means, a wavelength selection means, and a lightdistribution means which cooperate to transmit light substantiallyvertically through the samples, wherein the light comprises a firstcalibration wavelength, a second calibration wavelength and ananalyte-measuring wavelength, wherein the first and second calibrationwavelengths are different and within the near infrared wavelength regionof from 750 to 2500 nanometers and provide characteristic light signalvalues for each liquid sample, wherein there exists a predeterminedrelationship between the light signal values and the optical pathlengththrough the samples and wherein the analyte-measuring wavelengthprovides a characteristic analyte light signal value related to theconcentration of analyte present in each sample;

d. a detector for determining measured light signal values from lighttransmitted through each sample at the first and second calibrationwavelengths and the analyte-measuring wavelength;

e. a means for determining a measured relationship between the lightsignal values;

f. a means for determining from the measured relationship and thepredetermined relationship a correction factor related to the opticalpathlength through each sample;

g. a means for determining from the correction factor and the analytelight signal value, a ratio relating the analyte signal value to theoptical pathlength in each of the samples.

The invention also encompasses vertical-beam photometric devices formeasuring the rate of change in optical characteristics of samplescontained in sample sites disposed on an assay plate, the devicecomprising:

a wavelength selection means for selecting a first wavelength band oflight from a first wavelength range ad for selecting a second and athird wavelength bands of light from within a second wavelength range;

a sample-retaining means for retaining one, or more, samples, and alight-transmitting means for transmitting the light from the lightsource to the wavelength selection means and through the one, or more,sample;

a photodetector means for detecting the first, second and third bands oflight transmitted through a selected sample, and for providing a first,a second and a third signal in respective relationship to the first,second and third bands of light so transmitted;

a means for determining the optical pathlength of the first band oflight transmitted through the selected sample from the difference of thesecond and third signals; and

a means for relating the first signal to the optical pathlength sodetermined so as to determine and automatically indicate opticalparameters including either the absorbance or the fraction of incidentlight transmitted through the selected sample per unit opticalpathlength of the selected sample

and additionally a means for kinetic analysis of the signal of thephotodetector means relating to the selected site so as to determine therate of change of the optical parameters.

In another aspect, the invention provides multi-channel photometricanalysis devices for determining optical characteristics of analytes insets of liquid-containing samples having unknown optical pathlengths. Inthis aspect, the devices comprise:

a. a first sample holder for holding the sets of liquid-containingsamples in one or more substantially vertical optical channels;

b. a means for positioning the sets of samples in the optical channels;

c. a light source means, a wavelength selection means, and a lightdistribution means which cooperate to transmit light substantiallyvertically through the samples, wherein the light comprises a firstcalibration wavelength and a second calibration wavelength, wherein thefirst and second calibration wavelengths are different and within thenear infrared wavelength region of from 750 to 2500 nanometers andprovide characteristic light signal values for each liquid sample,wherein there exists a predetermined relationship between the lightsignal values and the optical pathlength through the samples;

d. a detector for determining measured light signal values from lighttransmitted through each sample at the first and second calibrationwavelengths;

e. a means for determining a measured relationship between the lightsignal values;

f. a means for determining from the measured relationship and thepredetermined relationship a correction factor related to the opticalpathlength through each sample;

g. a means for determining from the correction factor the opticalpathlength in each of the samples.

In another aspect, the invention provides methods for determining thevertical optical pathlength through a liquid-containing samplecomprising

a. placing the liquid-containing sample in a sample holder whichprovides a substantially vertical light path through the sample, saidvertical light path having an unknown optical pathlength through thesample;

b. transmitting light through the sample along the vertical light path,the light comprising a first calibration wavelength and a secondcalibration wavelength,

the first calibration wavelength and the second calibration wavelengthhaving different near infrared wavelengths within the range of from 750nanometers to 2500 nanometers to provide two characteristic light signalvalues for the liquid with a predetermined relationship between thevalues and the vertical optical pathlength through the sample;

c. determining measured light signal values at the first calibrationwavelength and at the second calibration wavelength;

d. determining from the measured light signal values, and thepredetermined relationship, the vertical optical light path pathlengththrough the sample.

In yet another aspect, the invention provides methods for determiningthe amount of analyte in a liquid-containing sample comprising

a. placing the liquid-containing sample in a sample holder whichprovides an unknown, substantially vertical, optical light path throughthe sample;

b. transmitting light through the sample along the vertical light path,the light comprising a first calibration wavelength, a secondcalibration wavelength, and an analyte-measuring wavelength,

the first calibration wavelength and the second calibration wavelengthhaving different near infrared wavelengths within the range of from 750nanometers to 2500 nanometers to provide two characteristic light signalvalues for the liquid with a predetermined relationship between thevalues and the vertical optical pathlength through the sample;

and the analyte-measuring wavelength providing a characteristic analytelight signal value related to the quantity of analyte present in thevertical optical light path;

c. determining measured light signal values at the first calibrationwavelength, the second calibration wavelength and at theanalyte-measuring wavelength, said measured light signal valuesresulting from the passage of the light through the sample;

d. determining a measured relationship between the measured light signalvalues at the first and second calibration wavelengths;

e. determining from the measured relationship and the predeterminedrelationship a correction factor related to the pathlength of thevertical light path through the sample;

f. determining from the correction factor and the measured light signalvalue at the analyte-measuring wavelength the amount of analyte in thesample.

In a further aspect, the invention provides photometric analysis systemsfor determining the vertical optical pathlength through aliquid-containing sample comprising

a. a sample holder into which the liquid-containing sample is placed andwhich provides a vertical light path through the sample where thevertical optical light path is unknown;

b. a light source which transmits light through the sample along thevertical light path, the light comprising a first calibration wavelengthand a second calibration wavelength wherein

the first and second calibration wavelengths are different and withinthe near infrared wavelength region of from 750 to 2500 nanometers andprovide two characteristic light signal values for the liquid with apredetermined relationship between the values and the vertical opticalpathlength through the liquid;

c. a detector for determining measured light signal values at the firstand second calibration wavelengths,

d. means for determining a measured relationship between the measuredlight signal values at the first and second calibration wavelengths; and

e. means for determining the vertical optical pathlength through thesample from the measured relationship.

In still another aspect, the invention provides a photometric analysissystem for determining the amount of an analyte in a liquid-containingsample the system comprising

a. a sample holder into which the liquid-containing sample is placed andwhich provides a vertical light path through the sample where thevertical optical light path is unknown; and

b. a light source which transmits light through the sample along thevertical light path, the light comprising a first calibrationwavelength, a second calibration wavelength and an analyte-measuringwavelength, wherein

the first and second calibration wavelengths are different and arewithin the near infrared wavelength region of from 750 to 2500nanometers and provide two characteristic light signal values for theliquid with a predetermined relationship between the signals and thevertical optical pathlength through the liquid, the analyte-measuringwavelength providing a characteristic analyte light signal value relatedto the quantity of analyte present in the vertical optical light path;

c. detector for determining measured light signal values at the firstand second calibration wavelengths and the analyte-measuring wavelength;

d. means for determining a measured relationship between the lightsignal values measured at the first and second calibration wavelengths;

e. means for determining from the measured relationship and thepredetermined relationship a correction factor related to the verticaloptical pathlength through the sample; and

f. means for determining the amount of the analyte in the sample fromthe correction factor and the measured light signal value at theanalyte-measuring wavelength.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph showing calibration of pathlength versus volume in aNUNC 96-well microplate.

FIG. 2 is a graph showing the results of measuring the optical densityof fractions at 490 nm in a vertical-beam photometer.

FIG. 3 is a graph of the results of measuring the optical density offractions at 490 nm in a vertical-beam photometer where the results havebeen corrected for the light absorption pathlength of each fraction soas to indicate optical density per unit (cm) optical pathlength of eachfraction.

FIG. 4 is a plot of total elution volume versus the optical densitymeasured at 490 nm for the combined volumes of the wells in a NUNC96-well microplate.

FIG. 5 is a graph showing the absorption spectrum of pure water between750 nm and 1100 nm at four different temperatures.

FIG. 6 is a graph of the near infrared (NR) portions of theelectromagnetic spectrum for a biological buffer solution, Dulbecco'sphosphate-buffered saline (PBS).

FIG. 7 is a graph of the results of the near infrared (NIR) portion ofthe electromagnetic spectrum for pure water and 0.1M, 0.5M and 1.0Mcitric acid solutions in pure water.

FIG. 8 is a graph of the results of the near infrared (NIR) portion ofthe electromagnetic spectrum, between 750 nm and 1100 nm, of either purewater, 0.1M, 0.5M or 1.0M sucrose solutions in pure water.

FIG. 9 is a schematic representation of the device of the presentinvention.

FIG. 10 is a schematic representation of a preferred embodiment of thepresent invention.

FIG. 11 is a schematic representation of a more preferred embodiment ofthe present invention.

DESCRIPTIONS OF THE PREFERRED EMBODIMENTS

The disclosed invention comprises photometric methods and devices fordetermining Light Absorption Pathlength of liquid samples containinganalytes dissolved or suspended in a solvent. The methods and devicesrely on determining a relationship between the light absorptionproperties of the solvent and the optical pathlength of liquid samplescontaining the solvent. This relationship is used to establish the LightAbsorption Pathlength for samples having an unknown Light AbsorptionPathlength, but having a similar solvent composition. Such samples, forexample, may be contained within a plurality of wells disposed in amultiassay plate, such as a 96-well microplate, in a vertical-beamphotometer. Such vertical-beam photometers are able to measureabsorbance of analytes within such samples at predetermined wavelengthsof light. According to the invention such vertical-beam photometers mayautomatically determine and indicate, to an analyst carrying out achemical measurement, the concentration of an analyte. The automaticdetermination is made, according to Equation (1), from (a) theabsorbance of the analyte in the sample, (b) the Light AbsorptionPathlength determined according to the invention, and (c) apredetermined “extinction coefficient of the analyte. In such a waynovel photometer devices automatically determine and indicate theconcentration of analytes in such multi-assay plates directly withoutemploying a standard curve.

Generally, the methods and devices of the invention rely on separatelydetermining light absorption by the solvent and, at a differentwavelength, light absorption by the analyte. Devices for carrying outthe methods particularly advantageously include vertical-beam absorbancephotometers with sample retaining means for containing samples disposedwithin the wells of multi-assay plates, wherein the photometer is ableto monitor light absorption of each sample at multiple wavelength bands,including bands in the visible or UV-visible region of the spectrum, aswell as bands in the near-infrared region of the electromagneticspectrum.

The invention, however, is not limited to photometers that measure lightabsorption solely. Rather the invention is useful generally invertical-beam photometers that measure optical characteristics insamples where the optical pathlength through a sample is not known butwhere it is desirable to know such optical pathlength. The inventionwill find general utility in vertical-beam photometers that,additionally, measure other optical properties of liquid samples,including, but not limited to fluorescence, phosphorescence,chemiluminescence, or light scattering. Thus the invention is useful forchemical measurement by vertical-beam photometers where the measurementis made by either light absorptivity, fluorometry, phosphorometry,chemiluminometry, turbidimetry (where the loss of light from the opticalpathlength is measured as optical density) and nephelometry (where thelight scattered off the optical axis is measured). When utilizing theinvention to measure optical properties of samples other than lightabsorbance, the invention will monitor light absorbance, of the solventin the sample, in combination with optical properties of the sampleother than light absorbance.

As used herein, A indicates an absorbance value measured according toEq. 1 and a subscripted value following A indicates the center of thebandpass spectrum of light (given in nanometers) that is used to makethe light-absorbance measurement. For example, (A₁₇₇₀−A₁₃₁₀) is themathematical difference between absorbance measurements, made on thesame sample with the same optical pathlength, with 1770 nanometer and1310 nanometer center bandpass incident light respectively. In certainsituations the fraction of incident light transmitted (I/I_(O)) may beemployed rather than the amount of light absorbance (logI_(O)/I) afteraccounting for the mathematical relationship between these twoparameters.

The solvents suitable for use in the invention and apparatus of theinvention may be any solvent although those absorbing light in thenear-infrared region are preferred. Particularly preferred solvents arethose having low ultraviolet and visible absorbance spectra. Suchsolvents are those typically having low electronic transitionprobabilities at energy levels corresponding to light of 180 to 750nanometer wavelength. For electronic transition probabilities of varioussolvents, see “High Purity Solvent Guide,” James T. Przybytek, ed.,1992, Burdick & Jackson Laboratories, Inc., Muskegon, Mich.

As used herein, the near-infrared portion of the electromagneticspectrum is that portion extending from about 750 to 2500 nanometers(ie., from about 0.750-2.5 microns wavelength or, in wavenumbers, about13,300-4000 cm⁻¹). Liquid water absorbs light with values of ε_(λ)·Cbetween 0.01 and 60 cm⁻¹ at absorption bands located within the nearinfrared region. At room temperature, the values of ε_(λ)·C for purewater is about 0.18 cm⁻¹ near 970 nanometers and is about 0.58 cm⁻¹ near1200 nanometers wavelength. These values may be found in Luck, Berichteder Bunsengesellschaft 67: 186-189, 1963; and Thomas et al., The Journalof Physical Chemistry 69:3722-2726, 1965.

The light absorption pathlength customarily employed in vertical-beamphotometry is between 1 millimeter and 1 centimeter.

According to Eq. 1, the values of Aλ at wavelengths of about 970nanometers and about 1200 nanometers are 0.018 or 0.058, respectively,for a 1 millimeter light absorption pathlength and 0.18 or 0.58,respectively, for a pathlength of 1 centimeter in pure water at roomtemperature. These values are well within the range of 0.01 to 4.0absorbance units which is generally desirable for precise opticaldensity measurements in vertical-beam photometers.

It has been unexpectedly discovered that near-infrared analysis of waterat selected wavelengths is sufficiently robust to give an inaccuracy ofless than 5% variation from the true pathlength value in vertical-beamphotometry. This discovery is surprising since: (1) absorption of lightby molecules in the near-infrared region (NIR) of the electromagneticspectrum is due to overtones or combinations of overtones originatingfrom fundamental absorption bands in the mid-infrared region extendingfrom 4000 to 600 cm⁻¹; (2) absorbance in the mid-infrared region is dueto intra-molecular bond stretching and bending vibrational motions andis highly dependent upon the extent of hydrogen bonding in aqueoussolutions; and (3) physical parameters such as temperature or ionicstrength, for example, influence the absorption coefficient andwavelength of maximum absorption. In addition, analytes present in watermay potentially influence hydrogen bonding within the solvent, thuschanging the light absorption properties of the water solvent. Theseproblems are discussed in the Handbook of Near-Infrared Analysis, DonaldA. Burns, Emil W. Ciurczak, eds., Marcel Dekker, Inc. 1992. See also, G.L. Kemeny and D. L. Wetzel, “Moisture: Study of a Lively Near-InfraredDiffuse Reflectance Spectrum, “Paper 117, FACSS 13^(th) Annual Meeting,Sept. 28-Oct. 3, 1986, St. Louis Mo.; and G. L. Kemeny and D. L. Wetzel,“Differences in the Spectrum of Water, “AACC Annual Meeting, Nov. 1-6,1987, Nashville, Tenn. Furthermore, samples analyzed by vertical-beamphotometry customarily have a curved meniscus and no single uniquepathlength exists for all rays of light passing through the sample.

The methods and apparatus of the invention may be used to determinevarious light absorption pathlengths within vertical-beam photometerscontaining samples, preferably light absorption pathlengths betweenabout 1 millimeter and 1 centimeter. Further, the invention may be usedwith a variety of solvents and analytes. Disclosed herein are fourembodiments suitable for determining light absorption pathlengths. Thesemethods and apparatus each utilize measurement of absorbance of thesample solvent in the near-infrared region of the electromagneticspectrum (NIR)

The first embodiment is especially well suited for use in determiningoptical pathlength in purely aqueous solvents within a moderatetemperature range. This embodiment may be used at temperatures fromabout room temperature to the temperature of the human body (i.e., fromabout 20 to 40° C.).

The second embodiment may be used to determine light absorptionpathlength for samples having an analyte in aqueous solvents over abroader range of temperatures, i.e., from about 0 to 100° C.

The third embodiment is suitable for determining light absorptionpathlength in mixtures of aqueous and non-aqueous solvents.

Finally, the fourth embodiment is preferred for use with nonaqueoussolvents having values of ε_(λ)·C of from about 0.05 to 5 cm⁻¹ forabsorption bands located within the near infrared to infrared regions ofthe electromagnetic spectrum from about 800 to 6000 nanometers.

Vertical-beam photometers suitable for carrying out the invention willhave the following:

1. a light source, such as tungsten halogen, xenon flash lamp, mercuryarc lamp, or the like;

2. a wavelength selection means capable of selecting bands of light inthe ultraviolet-visible region of the electromagnetic spectrum frombetween 180 to 750 nanometers. (These ultraviolet-visible bands willnormally be used for analysis of concentration of analytes in samplescomprised of at least one analyte dissolved in a solvent);

3. a wavelength selection means capable of selecting bands of light inthe infrared region of the electromagnetic spectrum greater than 750nanometers;

4. a light-distribution means, such as optical lenses and mirrors fordirecting light, or a system of fiber optics for directing the light;

5. a sample-retaining means for retaining samples disposed on amulti-assay plate, such as the NUNC 96-well microplate; and

6. a light detection means, such as photo-diodes, photo-conductioncells, a photo-multiplier, photo-Darlington cells, a diode-array, or thelike capable of detecting both the bands of the light in the ultravioletvisible region and the bands of light in the infrared region.

7. a means for determining the optical pathlength of the samples, asdescribed above.

Suitable wavelength selection means for both the ultraviolet-visibleregion and the infrared region of the electromagnetic spectrum includeoptical filters of colored glass, or the like, interference filters, ormonochromators for dispersing the light and selecting a band of light.With either filters or a monochrometer the bands of light desirably willbe narrow in the range of 1 to 25 nanometers bandwidth. Preferably thebands will be even narrower, but not so narrow as to unduly limit theamount of light provided, generally in the 5-10 nanometer range. Usuallythe wavelength selection means capable of selecting bands of light inthe infrared region will need to select bands of light only in thenear-infrared region of the electromagnetic spectrum from 750 nanometersto 2500 nanometers wavelength. Alternatively, a laser, such as ahelium-neon, argon ion, carbon dioxide, or solid state laser, e.g. aGaAlAs laser, could be used to fulfill both the requirement for a lightsource and a wavelength selection means. When more than one band ofwavelengths is desired, two, or more, lasers or light-emitting diodesmay be combined as the light source and the desired wavelength range maybe supplied by turning on the light source emitting the desiredwavelength band of light. Such lasers have the advantage of having highlight intensity at extremely narrow bandwidth. Alternatively,light-emitting diodes (LEDs) may be used to supply light of the desiredwavelength range. A variety of LEDs may be used selectively to providethe desired wavelength bands of light when switched from on to off.Alternatively, the LEDs or laser sources of light may be used inconjunction with a white light source, together with optical filters ora monochrometer. In this way, the wavelength range and intensity of thewhite light source may be extended at a desired wavelength.

A vertical-beam photometer suitable for monitoring the absorbance ofliquid samples in the ultraviolet-visible and the near-infrared portionsof the electromagnetic spectrum when fitted with the appropriateinterference filters, is described in U.S. Pat. Nos. 4,968,148 and5,112,134. A vertical-beam photometer disclosed in pending U.S. patentapplication Ser. No. 08/228,436 also would be suitable when fitted witha monochrometer capable of providing bands of light in the near-infraredportion of the electromagnetic spectrum. Such a monochomater is Part No.36-0504 available from Optometrics Inc., Ayer, Mass. All documents,e.g., patents and journal articles, cited above or below are herebyincorporated by reference in their entirety.

All documents, e.g., patents and journal articles, cited above or beloware hereby incorporated by reference in their entirety.

A particularly preferred instrument and software for carrying out thepresent invention is the SPECTRAmax®PLUS microplate spectrophotometer.In the following examples a SPECTRAmax®PLUS microplate spectrophotometerwas used and is available commercially from Molecular DevicesCorporation.

A schematic representation of the optical design of an apparatus of theinvention, as embodied in a SPECTRAmax®PLUS microplate spectrophotometeris shown in FIG. 11. Such a microplate spectrophotometer has a xenonflash lamp as a light source 102. Light produced by source 102 isdispersed by a monochrometer 110, having a diffraction grating 112, ontoa monochrometer exit slit 114. The selected light exiting through theexit slit 114 is resolved into wavelength bands of 2 nm (full width athalf-height) which are selectable in 1 nm increments between 190 and1000 nanometers by moving the angle of the grating 112 with respect tothe exit slit 114.

As shown in FIG. 11, nine optical fibers 120 are arranged linearly atthe exit slit to collect the selected light into 9 optical fiberchannels 122. Eight of the fiber channels 122 are used to direct theselected light to 8 individual channels of a vertical-beam photometerchamber 130 which is adapted to hold multi-assay plates 132. The platesare retained by a multi-assay plate housing 131 (not shown). The housingaccommodates multi-assay plates 135 such as standardized 96-wellmicroplates with sample wells in a 8×12 rectangular array, oralternatively, multi-well, linear, sample strips, such as standardized8-well strips. The optics 133 (not shown) of the vertical-beamphotometer chamber are adapted to allow the light to pass substantiallyvertically through fluid samples in the multi-assay plate 135 so as topass through a gas/liquid interface in each sample (i.e. passing througha meniscus) as is customary for vertical-beam photometry.

The remaining optical fiber is used to carry the selected light to acuvette housing 134 which is adapted to hold a rectangular cuvette 140or a rounded tube (e.g. a standard 1 cm pathlength optical cuvette ortest tube). The optics of the cuvette housing are adapted to allow thelight to pass through fluid samples in the cuvette without passingthrough a gas/liquid interface (i.e. without passing through a meniscus)as is customary for horizontal-beam photometry.

A first silicon photodetector 150 related to each optical fiber channelis positioned to collect light diverted by a beam-splitter 152positioned to reflect light before it has passed through the space wherethe fluid samples are placed (i.e., the sample position). A secondsilicon photodetector 154 related to each optical fiber channel ispositioned to collect the light after it has passed through the sampleposition. The ratio of photocurrents from the two photodetectors in eachchannel is used to compute the optical density of (or % transmission oflight passing through) the fluid samples (relative to a reference suchas air only in the sample position). This arrangement of photodetectorsis utilized both in cuvette housing 134 and the vertical-beam photometerchamber 130.

Cuvettes 140 are placed manually in cuvette housing 134 and fluidsamples are placed one-at-a-time in a cuvette 140 for optical densitymeasurements. In contrast, multiple samples may be placed in the wellsof multi-assay plates 132. Light from each of the 8 parallel opticalfiber channels passes simultaneously through up to 8 wells of amulti-assay plate allowing 8 simultaneous optical density measurementsin 8 different wells of the plate. A motorized plate carrier repositionsthe multi-assay plate so that subsequent groups of 8 wells areinterrogated by the 8 optical channels. In sequence, this process isrepeated until all samples have been interrogated, 8 at a time. Forexample, when a standard 96-well multi-assay plate with samples arrangedin a 8 rows×12 columns in a rectangular array is used, the plate carrierrepositions the multi-assay plate 12 times sequentially, so as tointerrogate simultaneously the 8 samples in each of the 12 columns.

For determination of optical pathlength of aqueous samples,near-infrared interference filters 160, mounted on a motor-driven filterwheel 162 (not shown) in monochrometer 110, are individually selectedand placed in the optical path of the microplate spectrophotometer. Theinterference filters are ½ inch diameter and have a 10 nanometerbandpass (nominally centered within 5 nanometers of 1000 nanometers andnear 900 nanometers, respectively). Light from the flash lamp passesthrough the filters and reflects off the optical grating and into theexit slit 114 having the optical fibers. Maximal light throughput isachieved when the optical grating 112 is placed at its “zero order”angle where light originating from the flash lamp is reflected into themonochrometer exit slit 114 without diffraction. The optical fibers 120direct the light to the individual channels of a vertical-beamphotometer chamber 130 and to the cuvette housing 134 as describedabove.

Alternatively, the grating 112 of monochrometer 110 may be positioned sothat bands of light centered within 5 nanometers of 1000 nanometercenter wavelength or 900 nanometer wavelength are diffracted onto exitslit 114 having optical fibers 122. In this alternative embodiment,optical filters 160 and filter wheel 162 are not needed. Also in thisalternative embodiment, the nominally 900 nanometer and 1000 nanometerbands of light directed into optical fibers 122 will have similarbandpass as other UV, visible and near infrared light diffracted bygrating 112 onto monochrometer exit slit 114 (in this example 2nanometers).

In still another alternative embodiment, the width of the monochrometerslit may be adjusted, either manually or automatically by an electricalapparatus such as a motor or solenoid, to provide a selected bandpass oflight. In this way a bandpass value may be selected for each centerwavelength of light. Generally bandpass values will be between 1nanometer and 10 nanometers. More generally bandpass values can bebetween 0.25 and 25 nanometers.

Optionally solvent (e.g. water) contained in a reference cuvette ofknown optical pathlength is used to calibrate the instrumentaldetermination of solvent pathlength. Cuvette 140 in cuvette housing 134may be used for this purpose. For example, light from the flash lamp ispassed through the 1000 nm interference filter and absorption by thesolvent in the reference cuvette is measured. Customarily, the combinedeffects of light reflectance and absorption are measured by comparisonof the light intensity transmitted through the solvent and the lightintensity transmitted through air (with neither the sample nor thesample retaining device, i.e. the cuvette, present). Next light from theflash lamp is passed through the 900 nm interference filter andabsorption by the solvent in the reference cuvette again is measured.Again, the combined effects of both light reflectance and absorption aremeasured by comparison of the light intensity transmitted through thesolvent and the light intensity transmitted through air (with neitherthe sample nor the sample retaining device, i.e., the cuvette, present).Loss of transmitted light due to reflection and absorption by thecuvette is approximately the same at the two wavelengths, thus thedifference in (calculated absorbance) values obtained in the twomeasurements gives the differential absorbance of substantially only thesolvent at the two wavelengths of light. The difference in absorbancevalues observed divided by the optical pathlength of the referencecuvette employed is the calibration value for this specific pair offilters. An experimental value of 0.1433 absorbance units/cm opticalpathlength was found for a specific 1000 nm/900 nm filter pair wherewater, between 15° C. and 37° C., is used as the solvent. This value isused in the examples described below. See Example 11.

One skilled in the art will recognize that modifications may be made inthe present invention without deviating from the spirit or scope of theinvention. The invention is illustrated further by the followingexamples which are not to be construed as limiting the invention orscope of the specific procedures described herein.

Experimental Measurements

a) Instrumentation:

A Theromax™ microplate reader, commercially available from MolecularDevices Corporation, Menlo Park Calif., USA, is used to make allvertical-beam photometry measurements. Nominally 1000, 900, and 970nanometer (center bandpass wavelength) inference optical filters may beobtained from Andover Corporation, Salem, N.H. Also, in this instance,the nominally 900 nanometer filter (Cat. No. 900FS10-25) is centered at902.6 nanometers with 11.5 nanometer bandpass (bandwidth at half maximaltransmittance). Also in this instance, the nominally 970 nanometerfilter (Cat. No. 970FS10-25) is centered at 970.0 nanometers and has 8.5nanometer bandwidth at half maximal transmittance. Other optical filterswere obtained as catalog items from Molecular Devices Corporation.Horizontal-beam photometric measurements, made for comparative purposes,are made in a Hewlett-Packard Model 8451A diode array spectrophotometerequipped with a 1 cm light path cuvette.

b) Reagents:

The following reagents may be obtained form Aldrich Chemical Co.,Milwaukee, Wis.: Acid Orange 8 (Cat. No. 21,453-1), Acid Orange 74 (Cat.No. 20,181-2), Azure B (Cat. No. 86,105-7), Direct Yellow 62 (Cat. No.20,206-1), Naphthal Green B (Cat. No. 11,991-1). Bromocresol Purple wasobtained from Sigma Chemical Co. (Cat. No. B-4263). The spectra of thesecompounds in the ultraviolet and visible regions of the electromagneticspectrum is given in, The Sigma-Aldrich Handbook of Stains, Dyes andIndicators, by Floyd J. Green, 1990 Aldrich Chemical Co., Inc.,Milwaukee, Wis. Durkee Yellow Food Color may be obtained from DurkeeFamous Foods SCM Corporation, Westlake, Ohio. Schilling Blue Food Colorwas obtained from McCormick & Co., Inc., P.O. Box 208, Hunt Valley, Md.Obtainable from Sigma Chemical Co. is PIPES (Piperazine-N,N′-bis[2-etharsulfonic acid]), sodium salt, Cat. No. P-6757.

c) Multi-assay plates:

For vertical-beam photometry, samples are contained within wells of a96-well microplate multi-assay plate. The microplates are Nunclon® Delta96-well, flat-bottom plates which may be obtained from VWR Scientific,Brisbane, Calif.

d) Experimental conditions:

Measurements reported in the below example were made at roomtemperatures between 20 and 25 degrees centigrade.

EXAMPLE 1

In this example a vertical-beam photometer was also used as ahorizontal-beam photometer in the near infrared at wavelengths greaterthan 800 nm. For these horizontal-beam measurements, a 1.00 cmpathlength quartz cuvette is filled with water and capped with a Teflon®stopper which is taped to the cuvette. The capped cuvette was placedhorizontally in a vertical-beam photometer so that a selected band ofincident light is passed through one clear (transparent) wall of thecuvette, next through the water sample, and finally through the oppositeclear (transparent) wall of the cuvette before being measured by thephotodetector of the photometer. The results of such measurements areequivalent to measurements made by horizontal-beam photometry. The bandof incident light is first selected by passing through either thenominally 900 nanometer center-band or the 970 nanometer center-bandinterference filter (each of which have approximately a 10 nanometerbandpass). The resulting photometric values were used as L Values ofI_(O) for each optical filter were obtained with neither the watersample nor the cuvette in the incident light path (air blank).Absorbance values are calculated by the photometer at each pre-selectedwavelength by using Eq. 1. The difference in absorbance values of the1.00 cm optical pathlength cuvette filled with water measured with thenominally 970 nanometer center-band filter used to provide incidentlight and the 900 nanometer center-band filter used to provide incidentlight (i.e. A₉₇₀−A₉₀₀) was found to be 0.180. Horizontal beam photometryat wavelengths less than 800 nm was performed with the Hewlett-PackardModel 8451 A spectrophotometer.

Next, similar measurements of (A₉₇₀−A₉₀₀) were performed on sixdifferent samples containing chromophoric analytes. Prior tomeasurement, the analytes were dissolved in the deionized water atconcentrations sufficient to yield samples having absorbance values ofbetween 1.0 and 3.0 absorbance units at their respective maximal lightabsorption wavelengths in the visible spectral region when placed in thesame 1 cm optical pathlength cuvette. The analytes are Acid Orange 8,Acid Orange 74, Azure B, Direct Yellow 62, Durkee Yellow Food Color. Thevalues of A₉₇₀−A₉₀₀ obtained experimentally for each of the analytes inaqueous solution range from 0.180 to 0.183. A similar measurement foranother analyte comprising Bromocresol Purple in a solvent mixture of 12mM PIPES (Piperazine-N,N -bis[2-ethanesulfonic acid]) and 38 mM SodiumPhosphate Buffer (1.0 parts 0.05 M PIPES: 3:14 parts 0.05 M SodiumPhosphate Buffer by volume, final pH=5.8), similarly was found to be0.183. From Eq. 1, and employing two absorbance measurements, A_(λ1),and A_(λ2), at two different wavelengths, (λ₁) and (λ₂), we have(A_(λ1)-A_(λ2))=(ε_(λ2)−ε_(λ1))·l·C. The value of (ε_(λ2)−ε_(λ1))·C forthese aqueous analytes at room temperature, is about 0.182 cm⁻¹. Basedupon this result, values of (ε₉₇₀−ε₉₀₀)·C within this range, predictablymight be employed generally to calculate light absorption pathlengthfrom measured values of (A₉₇₀−A₉₀₀) for a variety of aqueous samples(referred to as Sample A₉₇₀−A₉₀₀) at room temperature. According to thisprediction obtained from a small number of experimental samples, lightabsorption pathlength may be determined for aqueous samples attemperatures ranging from about 15 to 40° C., preferably about 23° C.,according to Eq. 2 with less than about 5% error as follows:$\begin{matrix}{{{Light}\quad {Absorption}\quad {Pathlength}} = \frac{{Sample}\quad \left( {A_{970} - A_{900}} \right)}{0.182\quad {cm}^{- 1}}} & (2)\end{matrix}$

Absorbance of samples per unit pathlength may be found by measuring theabsorbance, A_(x), of samples at a preselected wavelength, x, preferablynear the absorbance maximum of the analyte. The resulting values arereferred to as Sample A_(x) Light Absorbance per unit Pathlength inaqueous samples is calculated using equation 3, as follows:$\begin{matrix}{{{Light}\quad {Absorption}\quad {per}\quad {Unit}\quad {Pathlength}} = \frac{{Sample}\quad A_{x}\quad \left( {0.182\quad {cm}^{- 1}} \right)}{{{Sample}\quad A_{970}} - A_{900}}} & (3)\end{matrix}$

From these results and the temperature data provided in Berichte derBunsengesellschaft, supra, even greater precision may be obtained by a)measuring the temperature of the sample, or alternatively of the samplecompartment enclosing the aqueous sample, and b) adjusting the 0.182cm⁻¹ value [i.e., (ε₉₇₀−ε₉₀₀)·C] in the denominator of the right side ofEq. 2 and the numerator of Eq. 3 for the estimated temperature of thesample. For example, for aqueous samples at 2° C., the adjusted 0.182cm⁻¹ value would be about 0.157 cm⁻¹, for 10° C. about 0.168 cm⁻¹, for20° C. about 0.180 cm⁻¹, for 30° C. about 0.190 cm⁻¹, for 40° C. about0.200 cm⁻¹, for 50 °C. about 0.210 cm⁻¹, for 60° C. about 0.220 cm⁻¹,for 70° C. about 0.230 cm⁻¹, for 80° C. about 0.240 cm⁻¹ and for 90° C.about 0.250 cm⁻¹. Intermediate values of (ε₉₇₀−ε₉₀₀)·C for intermediatetemperatures may be obtained by interpolation.

In this example, the cuvette, filled with aqueous sample and sealed atthe top, was placed horizontally in the light beam of the vertical-beamphotometer without the use of any fixed retaining means. Thesehorizontal-beam photometric measurements made at the individual 970 and900 nanometer wavelengths varied by as much as ±0.050 absorbance unitsfrom measurement to measurement. The differential A₉₇₀−A₉₀₀ values,however, varied by no more than ±0.002 absorbance units. Thus, theA₉₇₀−A₉₀₀ value is relatively independent of the angle of the incidenttest light with respect to the sample cuvette in horizontal-beamphotometry. Differential measurements, such as the A₉₇₀−A₉₀₀ value,therefore function to eliminate errors due to variation of cuvette anglewith respect to the beam of test light in horizontal-beam photometry.Alternatively a fixed sample-retaining means would also help to reducesuch errors.

Next the same sample solutions were dispensed into the wells of a96-well microplate at sample volumes of 350, 300, 250, 200, 150, or 100μl per well. Each sample composition and volume combination was testedin 8 replicate wells of the microplate. Absorbance values for each wellwithin the microplate, with incident light passing substantiallyvertically through the wells, were measured in the vertical-beamphotometer at the same center-band wavelengths employed for therespective samples in the horizontal-beam spectrophotometermeasurements. “Solvent blank,” absorbance values of the pure watersolvent were also measured in the vertical-beam vs. an “air blank” ateach measurement wavelength. The appropriate “solvent blank” at eachcenter-band wavelength of incident light is subtracted from theexperimental absorbance measurements, which employed “air blank” valuesof I_(O) according to Eq. 1 above. These individual, “solvent blank”corrected absorbance values are determined for each analyte near itswavelength of maximal absorbance in each well of the microplate. Also,the optical pathlength (i.e. the light absorption pathlength) iscalculated from sample A₉₇₀−A₉₀₀ data obtained from each well in themicroplate according to Eq. 2 above. The individual, “solventblank”-corrected absorbance values determined for each analyte near itswavelength of maximal absorbance are then divided by the opticalpathlength for each well of the microplate. These values are termedspecific absorbance values. The specific absorbance values of eachanalyte (i.e., the absorbance per unit pathlength, reported in units ofcm⁻¹) are shown in Table I, below.

TABLE I Optical Density/Cm Pathlength Measured In A Vertical-BeamPhotometer vs. A Spectrophometer Absorbance per Centimeter PathlengthA/cm Microplate A/cm Microplate vs. [A/cm (cm⁻¹) 150-350 μlHorizontal-Beam Spectrophotometer Chromophore Microplate Volume Mean ±S.D. Spectrophotometer Difference (wavelength) 350 μl 300 μl 250 μl 200μl 150 μl 100 μl (cm⁻¹)(CV in %) (cm⁻¹) (cm⁻¹);(% diff.) Acid orange 82.37 2.33 2.32 2.33 2.34 2.37 2.34 ± 0.019 2.28 0.06 (2.5%) (490 nm) CV= 0.00% Acid Orange 74 1.59 1.59 1.59 1.59 1.59 1.61 1.59 ± 0.000 1.540.05 (3.2%) (480 nm) CV = 0.00% Azune B 1.43 1.44 1.44 1.46 1.45 1.471.44 ± 0.000 1.46 0.02 (1.0%) (650 nm) CV = 0.76% Blue Food Color 1.671.67 1.67 1.67 1.66 1.68 1.67 ± 0.004 1.66 0.01 (0.6%) (630 nm) CV =0.24% Bromcresol 1.15 1.15 1.17 1.16 1.16 1.18 1.155 ± 0.008 1.10 0.05(4.8%) Purple (420 nm) CV = 0.52% Bromoresol 0.996 0.992 1.008 0.9991.001 1.019 0.999 ± 0.006 0.955 0.04 (4.6%) Purple (590 nm) CV = 0.60%Direct Yellow 62 1.70 1.70 1.70 1.70 1.73 1.76 1.71 ± 0.013 1.70 0.01(0.4%) (340 nm) CV = 0.76% Yellow Food 2.67 2.62 2.59 2.59 2.59 2.612.61 ± 0.019 2.62 0.01 (0.3%) Color (420 nm) CV = 0.73%

As shown in Table I, the coefficient of variation (CV) for themeasurement of specific absorbance values, made at the five greatestsample volumes, for each of the seven different analytes, and made ateight different wavelenghts, was less than 1%. Further, even lowestvolume (100 μl) samples yielded acceptable specific absorbance results.The CV of the specific absorbance measurements for the 100 μl samples,however, slightly exceeded 1%. The reason for this increase in CV at thelowest volume (100 μl ) is that optimal precision in vertical-beamphotometers requires an optical density of 0.100, or greater. As shownin FIG. 1, in a typical 96-well microplate, a 100 μl volume only givesabout 0.2 cm optical (light absorption) pathlength. Employing therelationship shown in equation 2 above, we see that a 100 μl aqueousvolume in these microplates will produce only about 0.036 absorbanceunits in A₉₇₀−A₉₀₀ which is substantially less than the 0.100 requiredfor optimal precision.

Because there is diminished precision with such small sample volumes(between 10 and 100 μl) for example, in preferred embodiments, precisionof better than 1% may be obtained in determination of light absorptionpathlength by averaging multiple measurements of A₉₇₀−A₉₀₀.

Absorbance values measured in a horizontal-beam spectrophotometer withidentical sample solutions in a 1 cm light path cuvette are similar tothose obtained with the vertical-beam photometer, after correcting forthe determined optical (light absorption) pathlength.

Particularly preferred results are obtained when the concentration ofsolvent is relatively unchanged by the analyte. For example, theconcentration of water in one (1) molar sodium chloride aqueoussolution, at 0° C., is about 55.6, substantially the same (within 1%) asfor pure water at the same temperature. Thus, any optical property ofwater that is dependent upon the light absorption pathlength within thewater, as well as the water concentration, may be used to monitor theoptical pathlength within aqueous samples containing analytes, providedthat the optical property is otherwise unaffected by such analytes.

It is preferred, in most aqueous samples to maintain a highconcentration of the water solvent relative to the concentration of thedissolved analytes.

It is further preferred that absorbance measurements of the solvent notbe made exactly at the wavelength of maximal absorbance of the solvent.Instead, absorbance measurements are preferably made at a center-bandwavelength selected to be between a local maximum and a localtemperature isosbestic or “pseudo-isosbestic” point in absorbance of thesolvent in the NIR. Such temperature “pseudo-isosbestic” wavelengthsexist for light absorbance by solvents such as water. At suchtemperature “pseudo-isosbestic” wavelengths absorbance by the solvent isnearly independent of temperature.

In general, the wavelength where two absorbing chemical species inequilibrium have identical absorptive optical properties is called anisosbestic point. Such isosbestic points are often taken as evidence forthe existence of at least two inter-convertible absorbing forms of aspecies and which forms have overlapping absorption spectra. Forexample, the absorption spectra of simple pH indicator dyes, (e.g.Phenol Red) show isosbestic points as a function of pH. Phenol red, forexample, has an isosbestic point at 495 nanometers, where the protonatedform absorbs optimally close to 420 nanometers, and unprotonated form ofthe dye absorbs maximally at 560 nanometers wavelength. The equilibriumbetween the protonated and unprotonated forms of the dye shifts as afunction of temperature due to a non-zero ionization enthalpy of thedye. Thus, at this (wavelength) isosbestic point of Phenol Red will alsobe observed a temperature isosbestic point because although the relativeratio of unprotonated and protonated forms of the dye are temperaturedependent, the light absorptive properties of both forms of the dye aresubstantially unaffected by temperature variation.

In contrast, when two inter-convertible absorbing forms of a specieswith overlapping spectra exist but the measured optical property of atleast one of the individual chemical species is affected by a variable,the “perfect” isosbestic is destroyed. For example spectral narrowing orbroadening of an individual chemical species with temperature variationwill result in such a phenomenon. If the variation from a perfectisosbestic is slight, a “pseudo-isosbestic” is said to exist. Suchpseudo-isosbestic points are, in fact, observed in the near-infraredabsorptive properties of water, as a function of both temperature andionic strength variation. At both isosbestic and “pseudo-isosbestic”wavelengths the absorbance values of solvents are nearly unaffected bytemperature or hydrogen-bonding influences. Water, for example, hasmultiple “pseudo-isosbestic” wavelengths, with respect to temperaturevariations, which occur between about 980-1010 nanometers, again near1080-1120 nanometers, again near 1180-1200 nanometers, again near1280-1320 nanometers, again near 1440-1460 nanometers, and again near1750-1800 nanometers. Therefore, when the optical pathlength for aqueoussamples is determined from NIR absorbance measurements in these spectralregions, the variation in the results due to temperature andhydrogen-bonding variations from sample-to-sample, is minimized. It isfurther preferred that the following absorbance differences for water,(A₁₀₀₀−A₉₀₀), (A₁₁₉₀−A₁₁₀₀), (A₁₄₄₀−A₁₃₁₀), or (A₁₇₇₀−A₁₃₁₀) will bemeasured in order to determine the optical pathlength of aqueoussamples. It is preferred that the center bandpass wavelength be within10 nanometers of the pseudo-isosbestic or isosbestic wavelengths givenabove. It may be sufficient, however, for the center bandpass wavelengthin most cases to be within 20 nanometers.

The (A₁₀₀₀−A₉₀₀) absorbance differences are preferred NIR wavelengthsfor measuring absorbance with the silicon photodetectors present in the“Theromax” microplate reader employed for these measurements. Sincesilicon photodetectors do not provide reasonable detectivity atwavelengths substantially greater than 1100 nanometers, the (A₁₀₀₀−A₉₀₀)absorbance difference is selected as the absorbance difference of choiceto monitor the absorbance of water to obtain suitable absorbance valuesat the preselected wavelength with samples as small as 150 μl and toensure that the CV of the measurements are less than 1%. Alternatively,greater precision and less sensitivity to temperature and samplevariations can be obtained by providing vertical-beam photometers withlight detectors having good detectivity in the NIR region longer than1100 nanometers wavelength. Suitable detectors include, for example,thermal-type detectors, such as thermocouples, thermistor or pneumaticdevices. Alternatively, NIR semiconductor photodetectors, such asInGaAs, PbS, InAs, or Ge detectors, could be used. With these infraredphoto-detectors, any of the above other disclosed “pseudo-isosbesticpairs,” (A₁₁₈₅−A₁₁₀₀), (A₁₄₄₄−A₁₃₁₀), or (A₁₇₇₀−A₁₃₁₀), could be useddirectly to monitor the light absorbance pathlength of water. With suchalternative photodetectors, the (A₁₁₈₅−A₁₁₀₀) pair is most optimalbecause the absorbance of water at 1185 nanometers is about 0.545 per cmof pathlength, which is very nearly optimal for maximum signal-to-noiseratios in vertical-beam photometers employing light-absorbancepathlengths of from 0.2 cm to 1.0 cm.

A suitable wavelength bandpass (wavelength bandwidth at half-maximalintensity) for these measurements is about 10 nanometers. Bandpassvalues of from 0.5 to 15 nanometers are acceptable, narrower bandpassvalues restrict the intensity of available light unduly. Wider bandpassvalues result in undue loss in amplitude of differential absorbancemeasurements.

The isosbestic center bandpass wavelengths given in this example arepreferred. In practice, a range of center bandpass wavelengths, isacceptable for practice of the invention. Generally, for the 900 nmwavelength the acceptable center bandpass range is quite broad, fromabout 750 nm to about 925 nanometers. Generally, for the 1000 nmisosbestic wavelength, the acceptable center bandpass range is fromabout 980 nm to about 1020 nanometers. For the 1100 nm isosbesticwavelength, the acceptable center bandpass range is from about 980 nm toabout 1150 nanometers. For the 1190 isosbestic wavelength, theacceptable center bandpass range is from about 1175 nam to about 1210nanometers. For the 1310 nm isosbestic wavelength, the acceptable centerbandpass range is from about 1175 nm to about 1350 nanometers. For the1440 nm isosbestic wavelength, the acceptable center bandpass range isfrom about 1430 mn to about 1465 nanometers. For the 1700 nm isosbesticwavelength, the acceptable center bandpass range is from about 1720 nmto about 1820 nanometers. Further, the differences in absorbances at thegiven pairs of isosbestic wavelengths are preferred. It should berecognized, however, that any of the isosbestic wavelengths may bepaired with any other isosbestic wavelength in order to determine adifference in absorbance that is related to the pathlength of thesolvent (and which difference will be approximately independent oftemperature).

EXAMPLE 2

The method described in this example allows measurements of opticalpathlength with mixtures of aqueous and nonaqueous solvents. It alsoprovides for correction when substances, other than water (that mayabsorb at the NIR wavelengths selected to monitor optical pathlength invertical-beam photometry) are present in the solvent. In this examplethe differential NIR absorbance (A₉₇₀−A₉₀₀) is used to monitorpathlength in aqueous samples. Alternatively, the “pseudo-isosbesticpairs,” described above provide superior results under certainconditions. For example, the (Alooo-Agoo) pair will provide superiorresults with silicon photodetectors when the temperature is highlyvariable. The (A₁₁₈₅A₁₁₀₀) pair will provide superior results when thetemperature is variable and when a vertical-beam photometer is usedwhich employs photodetectors sensitive to light at wavelengths of 1100and 1185 nanometers in the NIR because larger absorbance values may beobtained with smaller light absorbance pathlengths. This method is asfollows:

1. Load the solvent employed (to dissolve the analyte) into a cuvette ofknown optical pathlength, for example, a 1 cm optical pathlengthcuvette. This pathlength is known as the Solvent Pathlength. Place thecuvette in a photometer and measure (A₉₇₀−A₁₀₀₀.) This parameter isreferred to as Solvent (A₉₇₀−A₉₀₀) (The cuvette may be stoppered andplaced on its side in the incident light path of vertical-beamphotometers in order to accomplish this step.)

2. Repeat part 1 in the same known optical pathlength cuvette, now withthe analyte of interest in the solvent. The resulting parameter isreferred to as Reference (A₉₇₀−A₉₀₀.) Also, measure, approximately, theabsorbance, A_(x), of the analyte at the wavelength which will be usedfor subsequent measurements of analyte concentration. This parameter isreferred to as Reference A_(x). Preferably, the concentration of theanalyte should be adjusted so that the absorbance of the analyte is avalue between 1.0 and 2.0.)

3. Measure the values of A_(x) in samples with the vertical-beamphotometer as is customary. These parameters are referred to as SampleA_(x). Also, measure (A₉₇₀−A₉₀₀) values of the samples with thevertical-beam photometer. The later parameter is referred to as Sample(A₉₇₀−A₉₀₀.) The light absorption pathlength in each of the samples isdetermined using equation 4 as follows: $\begin{matrix}{{{Light}\quad {Absorption}\quad {Pathlength}} = \frac{\quad {{{Sample}\quad \left( {A_{970} - A_{900}} \right)} - \left\{ {\frac{{Sample}\quad A_{\chi}}{{Reference}\quad A_{\chi}}{\left\lbrack {{{Reference}{{\left( {A_{970} - A_{900}} \right) - {{Solvent}\left. \left. \quad \left( {A_{970} - A_{900}} \right) \right\rbrack \right\}}}\quad}}} \right.}} \right.}}{\frac{{Solvent}\quad \left( {A_{970} - A_{900}} \right)}{{Solvent}\quad {Pathlength}}}} & (4)\end{matrix}$

Light Absorbance per unit Pathlength for the samples is determined fromequation 5 as: $\begin{matrix}{{{Light}\quad {Absorbance}\quad {per}\quad {unit}\quad {Pathlength}} = \frac{\frac{{Sample}\quad {A_{\chi} \cdot {Solvent}}\quad \left( {A_{970} - A_{900}} \right)}{{Solvent}\quad {Pathlength}}}{\quad {{{Sample}\quad \left( {A_{970} - A_{900}} \right)} - \left\{ {\frac{{Sample}\quad A_{\chi}}{{Reference}\quad A_{\chi}}\left. \left\lbrack {{{Reference}{{\left( {A_{970} - A_{900}} \right) - {{Solvent}{{\quad \left( {A_{970} - A_{900}} \right\rbrack}}}}}}} \right. \right\}}\quad \right.}}} & (5)\end{matrix}$

Preferably, the means for determining optical pathlength andautomatically determining and indicating light absorbance per unitpathlength (i.e., specific absorbance) are included in a vertical-beamphotometric device capable of monitoring the optical density of samplescontained in a multi-assay plate at a minimum of three (3) differentcenter-band wavelengths of incident light. The device preferably willinclude means for determining and indicating if the analyte presentssignificant interference with a simple, uncorrected, determination ofOptical Pathlength. An Interference Parameter is determined fromequation 6 as follows: $\begin{matrix}{{{Interference}\quad {Parameter}} = \frac{{Sample}\quad {A_{\chi}\left\lbrack {{{Reference}\quad \left( {A_{970} - A_{900}} \right)} - {{Solvent}\quad \left( {A_{970} - A_{900}} \right)}} \right\rbrack}}{{Reference}\quad {A_{\chi} \cdot \quad {Sample}}\quad \left( {A_{970} - A_{900}} \right)}} & (6)\end{matrix}$

Significant interference is deemed to be absent when the InterferenceParameter given by Eq. 6 is between 0.05 and −0.05, for example. Thus,the interference of the analyte creates less than a 5% error indetermination of Optical Pathlength. The device preferably will includeautomatic means for determining and indicating when any of theparameters Sample A_(x), Sample (A₉₇₀−A₉₀₀), Reference A_(x), Reference(A₉₇₀−A₉₀₀) or Solvent (A₉₇₀A₉₀₀) are less than 0.05 and, thus, too lowto provide an accurate estimation of interference or specificabsorbance.

Shown in Table II are the measurements of absorbance of Napthal Green Bin aqueous solvent samples determined according to the method set forthin this example above. For comparison purposes the results aredetermined according to Eq. (3) and according to Eq. (5). The LightAbsorbance per unit Pathlength measurements made (as described inExample 1) according to Eq. (3) in the vertical-beam photometer(microplate reader) were greater than the results obtained in thespectrophotometer by 101% (i.e. more than 2-fold greater). Eq. 5,however, provides results from the vertical-beam measurements with thevertical-beam photometer that are substantially identical to those fromthe horizontal-beam spectrophotometer.

TABLE II Light Absorbance/Cm Pathlength of an Interfering AnalyteDetermined with and without correction for the Optical Interference ofNapthal Green B Absorbance per Centimeter Pathlength A/cm MicroplateA/cm Microplate vs. ie. A/cm (cm⁻¹) 150-350 μl Horizontal-BeamSpectrophometer Naphthal Green B Microplate Volume Mean ± S.D.Spectrophotometer difference (725 nm) 350 μl 300 μl 250 μl 200 μl 150 μl100 μl (cm⁻¹)(CV in %) (cm⁻¹) (cm⁻¹)(% diff.) Uncorrected A/cm 2.40 2.392.40 2.41 2.44 2.51 2.41 ± 0.019 1.2 1.21 (+101%) (Eq. 3) CV = 0.08%Corrected A/cm 1.21 1.20 1.21 1.21 1.22 1.23 1.21 ± 0.07 1.20 0.01(+0.8%) (Eq. 5) CV = 0.06%

The procedure described in this example also allows Light AbsorptionPathlength and Light Absorbance per unit Pathlength to be determined formixtures of aqueous and nonaqueous solvents. Such mixture may include,for example, water, methanol, ethanol, propanol, acetone, acetonitrile,pyridine, glycerol, tetrahydrofuran, di-and trichlorobenzenes, orderivatives thereof, and organic esters such as methyl- orethyl-acetate. Any mixture of a nonaqueous, i.e., organic, and aqueoussolvent may be employed. Multi-assay plates that are resistant to suchsolvents include multi-assay plates made of glass, quartz, or otherpolymeric material resistant to nonaqueous solvents. Suitable quartz 8-or 96-well multi-assay plates are available from Hellena Laboratories,Beaumont Tex. and from Molecular Devices Corporation, Menlo, Park,Calif. (Part Nos. R1077 or R1076).

It should be readily apparent that absorbance of the aqueous solvent maybe measured at any of the isosbestic center bandpass wavelength pairsdescribed in example #1 above. For example, (A₁₀₀₀−A₉₀₀), or any othersuitable isosbestic center bandpass wavelength, could be usedadvantageously to eliminate temperature effects in the determination ofLight Absorption Pathlength, Light Absorbance per unit Pathlength, orInterference Parameter. The acceptable center bandpass ranges are thesame as described in example #1 above.

EXAMPLE 3

The method described in this example may be employed with any solvent,including solvents substantially free of water. For this method theabsorbance spectrum of the desired solvent is determined in the NIR. Twowavelengths are then selected, a first wavelength near an absorbancemaximum, denoted as A_(max), of the solvent; and a second wavelengthnear an absorbance minimum denoted as A_(min), of the solvent. Thedifference in absorbance of samples at the first and second wavelengths,(A_(max)−A_(min),) should preferably be selected to be between 0.050 and5.0. It is particularly preferred that the value of (A_(max)−A_(max)) beselected to be between 0.1 and 1.0. The method is conducted as follows:

1A. Load the solvent employed to dissolve the analyte into a cuvette ofknown (pre-determined) optical pathlength, for example, a 1 cm opticalpath cuvette. This optical pathlength is known as the SolventPathlength. Place the cuvette in a photometer and measure(A_(max)−A_(min).) This parameter is referred to as Solvent(A_(max)−A_(min).) (The cuvette may be stoppered and placed on its sidein the light path of a vertical-beam photometer in order to make thismeasurement.)

2A. Repeat step 1A, as described above in the same known opticalpathlength cuvette with the analyte of interest now in the solvent. Thisparameter is referred to as Reference (A_(max)−A_(min).) Also measure,approximately, the absorbance, A_(x), of the analyte at the wavelengthwhich will be used for subsequent measurements of analyte concentration.This parameter is referred to as Reference A_(x). Preferably, absorbanceof the analyte is between about 0.5 and 2.0)

3A. Measure the values of A_(x) in samples with the vertical-beamphotometer. These parameters are referred to as Sample A_(x). Alsomeasure (A_(max)−A_(min)) values of the samples with the vertical-beamphotometer. The later parameter is referred to as Sample(A_(max)−A_(min)).

The light absorption pathlength in each of the samples is determinedfrom equation 7 as follows: $\begin{matrix}{{{Light}\quad {Absorption}\quad {Pathlength}} = \frac{\begin{matrix}{{{Sample}\left( {A_{\max} - A_{\min}} \right)} -} \\\left\{ {\frac{{Sample}\quad A_{x}}{{Reference}\quad A_{x}}\left\lbrack {{{Reference}\left( {A_{\max} - A_{\min}} \right)} - {{Solvent}\left( {A_{\max} - A_{\min}} \right)}} \right\rbrack} \right\}\end{matrix}}{\frac{{Solvent}\left( {A_{\max} - A_{\min}} \right)}{{Solvent}\quad {Pathlength}}}} & (7)\end{matrix}$

Light Absorbance per unit Optical Pathlength for samples is determinedusing equation 8: $\begin{matrix}{{{Light}\quad {Absorbance}\quad {per}\quad {unit}\quad {Pathlength}} = \frac{\frac{{Sample}\quad {A_{\chi} \cdot {{Solvent}\left( {A_{\max} - A_{\min}} \right)}}}{{Solvent}\quad {Pathlength}}}{\begin{matrix}{{{Sample}\left( {A_{\max} - A_{\min}} \right)} -} \\\left\{ {\frac{{Sample}\quad A_{\chi}}{{Reference}\quad A_{\chi}}\left\lbrack {{{Reference}\left( {A_{\max} - A_{\min}} \right)} - {{Solvent}\left( {A_{\max} - A_{\min}} \right)}} \right\rbrack} \right\}\end{matrix}}} & (8)\end{matrix}$

In general, this method provides for determining the absorbance of ananalyte per unit light absorption pathlength (or fraction of lighttransmitted by an analyte per unit light absorption pathlength) whereinthe analyte is suspended or dissolved in a liquid solvent such that arelationship between light absorption of the analyte and the lightabsorption pathlength of the analyte are unknown. This method alsoprovides for determination of the concentration of the analyte accordingto Equation (1) from (a) the absorbance of an analyte in the sample, (b)the light absorption pathlength of sample, and (c) a predeterminedextinction coefficient of the analyte. If the analyte interferes withdetermination of the light absorption pathlength, or if solvents otherthan water are present, the relationship between absorbance of thesolvent and absorption pathlength (or the amount of interference) may bequantitated, thus allowing a correct light absorption pathlength to bedetermined.

In general, a first, a second and a third light signal resulting from,respectively, a first, second, and third predetermined wavelength oflight transmitted through substantially identical optical pathlengthwithin a sample and wherein a difference between the first and thesecond light signals (e.g. A₉₇₀−A₉₁₀) is related to the light absorptionpathlength and the third light signal (e.g. A₄₉₀ where Acid Orange 8 isthe analyte) is related to both the light absorption pathlength and theconcentration of the analyte. The light absorption properties of thesample solvent may be determined, independently of the analyte bymeasuring a forth and fifth light signal (e.g. A₉₇₀ and A₉₁₀) resultingfrom, respectively, the first and the second wavelength of lighttransmitted through a predetermined optical pathlength (e.g. 1 cm) ofthe solvent which is employed as a first reference liquid. Comparison ofthe difference in the first and second light signals (e.g. A₉₇₀−A₉₁₀ ofthe sample) and the forth and fifth light signals (e.g. A₉₇₀−A₉₁₀ of thesolvent) allows the known light absorption pathlength of the solvent tobe compared directly to the unknown light absorption pathlength of thesample.

Provided that the sample does not interfere with determination of thelight absorption pathlength, the concentration of the analyte may bedetermined form absorbance of the sample at the third wavelength (e.g.A₄₉₀, where Acid Orange 8 is the analyte) or the fraction of lighttransmitted at the third wavelength per unit light absorptionpathlength, from the predetermined light pathlength, the third lightsignal, the difference in the first and second light signal and thedifference in the fourth and fifth light signals.

When the sample interferes with determination of the light absorptionpathlength, the concentration of the analyte may be determined bymeasuring a relationship between absorbance of the analyte at the thirdwavelength and its (interfering) absorbance at the first and secondpredetermined wavelengths. Thus, a second reference liquid, containingthe analyte, is prepared and used to measure a sixth and a seventh lightsignal resulting from, respectively, the first and second predeterminedwavelengths of light transmitted through a predetermined lightpathlength of the second reference liquid (e.g. A₉₇₀−A₉₁₀ of the secondreference solution). The second reference liquid also is used to measurean eight light signal at the third predetermined wavelength (e.g. A₄₉₀,where Acid Orange 8 is the analyte) in a predetermined pathlength. Theeffect of sample interference may be eliminated substantially fromdetermination of light absorption pathlength according to the example asshown in equation 7. Similarly the effect of sample interference may beeliminated substantially from determination of light absorption per unitpathlength according to the example shown in Equation 8. Thus, the lightabsorption pathlength, light absorption per unit pathlength, fraction oflight transmitted per unit pathlength, or concentration of analyte(according to Equation 1) may be determined from the predeterminedoptical pathlength and from the first, second, third, fourth, fifth,sixth, seventh and eighth light signals.

Preferably, the means for determining Light Absorption Pathlength andfor determining and indicating Light Absorbance per unit OpticalPathlength automatically are included in a vertical-beam photometricdevice capable of monitoring the optical density of samples contained ina multi-assay plate at a minimum of three (3) different center-bandwavelengths of light. The device preferably will include means fordetermining and automatically indicating if the analyte presentssignificant interference with a simple, uncorrected, determination ofLight Absorption Pathlength. An Interference Parameter, is determinedusing equation 9 as follows: $\begin{matrix}{{{Interference}\quad {parameter}} = \frac{{Sample}\quad {A_{x}\left\lbrack {{{Reference}\left( {A_{\max} - A_{\min}} \right)} - {{Solvent}\left( {A_{\max} - A_{\min}} \right)}} \right.}}{{Reference}\quad {A_{x} \cdot {{Sample}\left( {A_{\max} - A_{\min}} \right)}}}} & (9)\end{matrix}$

There are a variety of uses for the methods and devices of theinvention. For example, the volume of samples collected from afraction-collector in the wells of a multi-assay plate may be desired.In such a determination, the relationship between Sample Volume andLight Absorption Pathlength would be first determined according to anyone of the methods provided above. This procedure is carried out in thefollowing example.

EXAMPLE 4

The data established in Example 1 above were used to determine therelationship between Light Absorption Pathlength and Sample Volume inthe Nunclon® Delta 96-well, flat-bottom multi-assay plates utilized inthat Example. Measurements of A₉₇₀−A₉₀₀ were performed on six differentchromophoric analytes, Acid Orange 8, Acid Orange 74, Azure B, DirectYellow 62, Durkee Yellow Food Color, and Schilling Blue Food Color, inaqueous solvent. The sample solutions were dispensed into the wells ofthe multi-assay plate at either 350, 300, 250, 200, 150, or 100 μlsample volume per well. Each sample and volume combination was tested in8 replicate wells of the microplate.

The values of Sample (A₉₇₀−A₉₇₀) obtained experimentally were used todetermine Light Absorption (i.e., optical) Pathlength for each wellaccording to Eq. 2. FIG. 1 shows the volume of sample pipetted into eachwell vs. the mean Light Absorption Pathlength so determined and averagedfor all of a given volume. The result shows that, for the 96-well NUNCmicroplate, the linear relationship described by equation 10 isobserved:

 Light Absorption Pathlength=[(2.82 cm/ml) (Sample Volume)]−0.0612cm  (10)

The correlation coefficient for this linear relationship was 0.9999. Theinverse of this relationship is described by equation 11 for a 96-wellNUNC microplate as follows: $\begin{matrix}{{{Sample}\quad {Volume}} = \frac{\left( {{{Light}\quad {Absorption}\quad {Pathlength}} + {0.0612\quad {cm}}} \right){ml}}{2.82\quad {cm}}} & (11)\end{matrix}$

Equation 11 may be used to determine the approximate volume containedwithin the wells of such a multi-assay plate upon determining the LightAbsorption Pathlength of the samples. Further, with suitablecalibration, this procedure may be used to determine the volumecontained in the wells of any type of assay plate. The wells of themicroassay plates may be of various geometric shape, includingflat-bottom, round-bottom (U-bottom), V-bottom, or any other shape. Anygeometry or shape of wells in the multi-assay plate may be employed aslong as the relationship between sample volume from the Light AbsorptionPathlength is substantially reproducible (generally within 5%). Therelationship need not be linear, as is shown above for NUNC microplateswhich have cylindrical (flat-bottom) wells. It is only necessary todetermine this relationship utilizing a multiplicity of known volumes ofsamples, and then determining Light Absorption Pathlength for thesamples of known volume. This relationship may be used subsequently,together with Light Absorption Pathlength determinations in individualwells of multi-assay plates to estimate the liquid volume present withinsuch plates.

EXAMPLE 5

This example demonstrates utility of the invention in the field ofchromatography. Chromatography is used, generally, to separate analytecomponents in a sample mixture. Generally in chromatography, thereexists a mobile phase and a stationary phase. The sample is applied inthe mobile phase at the input of a means of retaining the stationaryphase, e.g. a tubular column with a mesh support at the output of thecolumn. As the mobile phase passes over the stationary phase theanalytes bind to the stationary phase for more, or less time, dependingon their affinity for the stationary phase, and therefore appear atdifferent times at the output of the column. Separation of analytes in asample is thereby accomplished when, “fractions” of the mobile phase, atthe output of the column, are collected over time. In chromatography,generally, one wishes to analyze the amount, or concentration, ofanalyte present in each fraction collected. Furthermore, forreproducible chromatographic systems, carried out under constantconditions, (e.g. constant temperature, constant stationary phase,constant mobile phase, constant flow rate, constant column volume,etc.,) the same analyte will usually appear at the same “elutionvolume,” (i.e. after the same volume of mobile phase has passed throughthe column). For such reproducible systems, one generally wishes to havea plot of the relative concentration of each analyte as a function ofelution volume. The below example discloses utility of the instantinvention in obtaining such “chromatograms” simply and convenientlywhile employing a vertical-beam photometer.

Certain, commercially-available fraction collectors may be employedconveniently to collect fractions directly in the wells of 96-wellmicroplates such as the NUNC microplate employed above. For example, onesuch fraction collector is manufactured by the Gilson Corporation,Middleton, Wis. Generally, such fraction collectors collect fractionsfor a given time interval, or alternatively, such fraction collectorsmay count the droplets at the output of the chromatographic column andeach fraction may contain a certain predetermined number of droplets.One problem is that each fraction contains a different, and unknownvolume whenever the flow rate is not maintained constant for the timeinterval method, and whenever the surface tension of the mobile phase isnot maintained constant for the drop-counting method. Therefore,analysis of the fractions collected in a multi-assay plate byvertical-beam photometry will give absorbance values for each fractionthat will be influenced both by the concentration of analyte present andby the volume of analyte present in the sample. The two variables,concentration and volume, thereby are confounded and a method fordetermining the two variables separately is needed. One method of theprior art is to manually measure the volume of each fraction, towithdraw a known volume from each well to transfer the withdrawn volumeinto a second multi-assay plate and to measure the optical density ofeach well in the second multi-assay plate. This prior art proceduresuffers from the disadvantage that it is tedious, cumbersome, and proneto errors made during the volume-measuring and transferring steps. Themethod described below provides for a less tedious and cumbersomeprocedure and may be automated so as substantially to avoid errors.

In the present example, immunoglobulin (IgG) protein molecules werecovalently-labeled with a fluorescent, fluorescein moiety. The reagentfor labeling the protein was an NHS ester of fluorescein as provided inthe Immuno-Ligand Assay Labeling Kit, Cat. No. R9002, Molecular DevicesCorp., Menlo Park, Calif. The IgG was reacted with the labeling reagentat 40:1 molar ratio of reagent to protein in pH 7.0 phosphate-bufferedsaline (PBS) according to the instructions provided by the commercialsupplier of the reagent. The reaction product, in 0.3 ml volume, wasapplied to a PD-10 column containing G-25 Sephadex® gel filtration media(Pharmacia, Uppsula Sweden) as the solid phase. The column was elutedwith 0.1 ml aliquots of PBS applied successively to the top of thecolumn. Each fraction was collected, into a separate well of a NUNC96-well microplate, from the time of application of each 0.1 ml aliquotof PBS until the column ceased to flow. After the flow ceased, theoutput of the column was switched to a new well of the microplate andthe next aliquot of 0.1 ml of PBS was applied and the next fractioncollected, etc.

FIG. 2 shows the results of measuring the optical density of eachfraction at 490 nanometer wavelength in a Spectramax 250 vertical-beamphotometer (Molecular Devices Corporation, Menlo Park, Calif.). Thefirst fraction was collected for analysis after discarding the first 1.5ml of PBS collected from the column. As seen in FIG. 2, a maximum inOD₄₉₀ was observed at fraction 17 where the labeled protein eluted fromthe column, as determined by similarly measuring the optical density ofthe fractions at 280 nanometers, which also shows a maximum inabsorption of fraction 17. Unreacted labeling reagent eluted from thecolumn in subsequent fractions are not shown in the figures. The shapeof the curve shown in FIG. 2 is somewhat irregular. This irregularity,apparently, is not due to irregular variation in the concentration ofIgG but is due to irregularity in the optical pathlength of theindividual fractions. Shown in FIG. 3 are the same data corrected forlight absorption pathlength of each fraction. The shape of the elutionpattern of the labeled protein appears much more regular in FIG. 3,where the OD₄₉₀ per cm pathlength (i.e., the specific OD₄₉₀) is plottedfor each fraction compared to FIG. 2 where only the OD₄₉₀ is shown. Thelight absorption pathlength in each fraction was determined bymonitoring the difference in absorbance at 970 and 900 nanometercenter-band pass wavelengths of near-infrared light in the Theromaxvertical-beam photometer and calculated according to equation 2.

Further shown in FIG. 4 are the same data shown in FIG. 3, except thatthe cumulative volume (after the first 1.5 ml. eluted from the column)appears on the ordinate of the plot. The cumulative volumes weredetermined by employing the relationship of Equation 11, established forPBS in NUNC 96-well flat bottom microplates, to determine the volume ofeach fraction from the measured optical density difference at 970 and900 nanometer center-band pass wavelength and the light absorptionpathlength values calculated from these data and equation 2. The volumesof each subsequent fraction then were summed to determine the cumulativeelution volume. Each OD₄₉₀ per cm optical pathlength point is plotted atthe mean cumulative elution volume of an individual fraction.

EXAMPLE 6 Elimination of error in Determination of Optical Pathlengthdue to Variation in Solvent Temperature

Data have been gathered for a series of aqueous biological buffersolutions, which now permit further optimization of wavelength selectionin the near infrared portion of the electromagnetic spectrum (“NIR”) foruse in determining optical pathlength of samples dissolved in suchaqueous buffers. The NIR portion of the electromagnetic spectrum extendsfrom 750 to 2500 nanometers wavelength. In this NIR range, lightdetection means may be detectors made of indium-gallium arsenide;gallium arsenide, germanium, cadmium sulfide, lead sulfide, or the like.Preferably the measurement wavelengths will be between 750 and 1100nanometers so that silicon photodetectors may be used as a lightdetection means. Silicon photodiodes generally are useful in the rangeof 180 nanometers to 100 nanometers wavelength.

The following reagents were prepared: One-tenth molar (0.1 M)N-[2-Hydroxyethyl] piperazine-N′-[2-ethanesulfonic acid] (HEPES) wasprepared from HEPES (1.0M) obtained from Sigma Chemical Co., St. LouisMo. (Cat. No. H0887), by dilution into de-ionized water. One-tenth molar(0.1 M) Tris(hydroxymethyl) aminomethane (TRIS), pH 7.12, was preparedfrom 1.0 M TRIS obtained from BioRad Laboratories, Hercules, Calif.(Cat. No. 161-0719) by dilution into de-ionized water. The 0.1 M sodiumphosphate was prepared by mixing 61 ml of 1.0 M sodium phosphatemonobasic, (Cat. No. S369-1) and 39 ml of sodium phosphate dibasic,(Cat. No. S374-500) each from Fisher Scientific Pittsburgh, Pa. anddiluting into de-ionized water. Threshold Assay Buffer was prepared bydilution of Concentrated (10×) Threshold Assay Buffer obtained fromMolecular Devices Corporation, Sunnyvale, Calif. (Cat. No. R3030-1) anddiluted to 1×(pH 57.02) in de-ionized water. Dulbecco's phosphatebuffered saline solution, pH7.3 (PBS), was obtained from IrvineScientific (Cat. No. 9236). One-tenth molar (0.1M)2[N-Morpholino]ethanesulfonic acid (MES) buffer, pH 6.14, was preparedfrom MES obtained from Sigrna Chemical Company (Cat. No. M-8250) indeionized water.

FIG. 5 shows the absorption spectrum of pure water between 750 and 1100nanometers at 4 different temperatures, i.e. 14° C., 23° C., 35° C. and44° C. The spectra were taken in an ATI Unicam UV-2-100 Double BeamScanning UV-Visible Spectrometer with a 2.0 nanometer fixed bandwidth.The data were taken under the control of a Compaq 386 computer runningATI Vision software set to take spectral data in the “Survey” mode at“Intelliscan” speed. Approximately 3 ml samples were placed in SpectroClear™ Acrylic precision spectrophotometer cuvettes, with a lightabsorption pathlength of 1.00 cm, obtained form Centaur Science, Inc.,Stamford, Conn., (Cat. No. SCA-20) in the sample beam of thespectrophotometer. The reference beam contained no sample or cuvette.(Measurements made in this configuration are said to employ an “airblank”).

FIG. 5 also shows that between 900 and 917 nanometers there isrelatively little absorbance of the water sample. Between 960 and 980nanometers there is a peak of maximal absorbance of the water sample.The wavelength of maximal absorbance (λ_(max)), as well as theabsorbance at λ_(max), changes as a function of temperature. Forexample, at 974 nanometers which is near λ_(max), the absorbance changesby about 0.4% per degree centigrade. Thus, in order to obtain +/−1%precision in determination of optical pathlength, the temperature mustvary by no more than +/−2.50° C.

In contrast, at about 998 nanometers pure water gave constant opticaldensity of about 0.14 at all four temperature values. Thus, thewavelength region near 998 nanometers (e.g. the wavelength region from988 to 1008 nanometers) is a region where optical properties of purewater are nearly independent of temperature. For the present, we shallcall such a wavelength region an “isosbestic wavelength region” whichfor pure liquid water occurs near 998 nanometers as a function oftemperature.

FIG. 6 similarly shows the NR absorption spectrum of Dulbecco'sphosphate-buffered saline (PBS) containing 200 mg/l potassium chloride,200mg/l potassium phosphate monobasic, 8000 mg/1 sodium chloride and1158 mg/l sodium phosphate dibasic, pH 7.23 which is a commonly-usedbiological buffer solution. The absorption spectrum is strikinglysimilar to that of pure water seen in FIG. 5. The NIR absorptionspectrum for isotonic (0.155 M) sodium chloride; 0.1 M phosphate, pH 7.0and 0.1 M TRIS, 0.1 M HEPES, 0.1 M MES and Threshold Assay Buffersimilarly were recorded at 14° C., 23° C., 35° C. and 44° C. In eachcase the NIR absorption spectra (not shown) are virtuallyindistinguishable from that of pure water (i.e. less than 3% differentin relative absorption intensity any wavelength). The isosbesticbehavior, as a function of temperature, in each case is observed near998 nanometers.

Table III shows optical density values, determined at several selectedwavelengths, each at the 4 selected temperature values, for each aqueousbuffer solution. Also shown in Table III are the results of taking thedifference in optical density measured at 998 nanometers and opticaldensity measured at either 900 or 910 nanometers, i.e., (OD₉₉₈−OD₉₀₀) or(OD₉₉₈−OD₉₁₀) for each aqueous buffer solution at each temperature. Theresults show that for the 8 different samples, the (OD₉₉₈ and OD₉₀₀) and(OD998−OD₉₁₀) were remarkably constant at all temperature values. The(OD₉₉₈−OD₉₀₀) values ranged from 0.138 to 0.133, i.e. a range of 3.6%.The (OD₉₉₈−OD₉₁₀) values ranged from 0.135 to 0.132. i.e. a range of2.9%. Thus interference or inaccuracies in determining opticalpathlength though liquid samples can be eliminated substantially by:

1.) measuring a first optical density value of the samples in a first“isosbestic wavelength region”,

2.) measuring a second optical density value of the samples in a second“isosbestic wavelength region”, and

3.) determining the difference in the first and second optical densityvalues.

Preferably, the absorption coefficient of the sample is substantiallydifferent in the first and second wavelength regions. For example, asshown in FIGS. 5 and 6 and Table III, for aqueous samples a “isosbesticwavelength region” occurs about 998 nanometers (generally from 993 to1002 nanometers, and more generally from 988 to 1008 nanometers). Asecond isosbestic wavelength region occurs about 910 nanometers(generally from 900 to 910 nanometers, and more generally from 750 to930 nanometers). Alternatively, a second isosbestic wavelength regionoccurs near 1090 nanometers (generally from 1080 to 1100 nanometers andmore generally from 1050 to 1150 nanometers).

TABLE 3 0.1 M 0.9% NaCl 1xThreshold Phosphate dH20 (Saline) 0.1 M HEPESAssay Buffer 0.1 M TRIS 1xPBS Buffer 0.1 M MES 14° C. 900 0.075 0.0720.072 0.070 0.074 0.072 0.071 0.076 910 0.075 0.073 0.073 0.071 0.0750.073 0.072 0.077 974 0.240 0.237 0.235 0.236 0.238 0.238 0.236 0.239976 0.241 0.239 0.236 0.237 0.239 0.239 0.237 0 240 978 0.242 0.2390.236 0.237 0.239 0.239 0.237 0.241 980 0.241 0.239 0.236 0.237 0.2390.240 0.237 0.240 982 0.240 0.238 0.235 0.236 0.239 0.239 0.237 0.240998 0.222 0.220 0.218 0.217 0.221 0.220 0.218 0.222 1000  0.219 0.2160.214 0.214 0.218 0.217 0.215 0.219 998-900 0.147 0.148 0.146 0.1470.147 0.148 0.147 0.146 998-910 0.147 0.147 0.145 0.146 0.146 0.1470.146 0.145 23° C. 900 0.073 0.072 0.072 0.069 0.073 0.072 0.071 0.075910 0.075 0.072 0.073 0.070 0.074 0.073 0.072 0.076 974-976 0.250 0.2480.245 0.246 0.248 0.248 0.247 0.249 976 0.250 0.248 0.245 0.246 0.2490.249 0.247 0.250 978 0.250 0.248 0.245 0.245 0.249 0.248 0.246 0.249980 0.249 0.247 0.244 0.245 0.247 0.247 0.245 0.248 982 0.247 0.2450.243 0.243 0.246 0.246 0.244 0.247 998 0.223 0.220 0.218 0.218 0.2220.221 0.219 0.222 1000  0.219 0.216 0.214 0.214 0.218 0.216 0.215 0.219998-900 0.150 0.148 0.146 0.149 0.149 0.149 0.148 0.147 998-910 0.1480.148 0.145 0.148 0.148 0.148 0.147 0.146 35° C. 900 0.073 0.071 0.0720.069 0.073 0.071 0.071 0.074 910 0.075 0.072 0.073 0.070 0.074 0.0720.073 0.076 974 0.262 0.259 0.256 0.258 0.260 0.260 0.260 0.262 9760.262 0.259 0.256 0.257 0.260 0.260 0.259 0.261 978 0.260 0.258 0.2550.256 0.259 0.258 0.258 0.260 980 0.258 0.256 0.253 0.254 0.256 0.2560.255 0.257 982 0.256 0.253 0.250 0.251 0.254 0.253 0.253 0.255 9980.223 0.220 0.218 0.218 0.222 0.220 0.220 0.222 1000  0.218 0.215 0.2130.213 0.217 0.216 0.215 0.217 998-900 0.150 0.149 0.146 0.149 0.1490.149 0.149 0.148 998-910 0.148 0.148 0.145 0.148 0.148 0.148 0.1470.146 44° C. 900 0.073 0.070 0.071 0.069 0.072 0.071 0.071 0.074 9100.075 0.072 0.072 0.071 0.074 0.072 0.072 0.076 974 0.271 0.268 0.2650.266 0.269 0.268 0.268 0.270 976 0.269 0.266 0.264 0.265 0.267 0.2670.267 0.269 978 0.267 0.264 0.262 0.263 0.266 0.265 0.264 0.267 9800.265 0.262 0.259 0.260 0.263 0.262 0.261 0.264 982 0.261 0.258 0.2560.257 0.259 0.259 0.258 0.260 998 0.222 0.220 0.218 0.218 0.222 0.2200.219 0.222 1000  0.217 0.214 0.212 0.212 0.216 0.215 0.214 0.216998-900 0.149 0.150 0.147 0.149 0.150 0.149 0.148 0.148 998-910 0.1470.148 0.146 0.147 0.148 0.148 0.147 0.146

When employing (OD₉₉₈−OD₉₁₀) values to measure optical pathlength, avalue of 0.135 cm⁻¹ (generally from 0.140 to 0.130 cm⁻¹) may be used tocalculate optical pathlength through substantially aqueous samples. Forexample, if a (OD998−OD₉₁₀) value of 0.135 is determined for aqueoussamples with an unknown optical pathlength, the unknown opticalpathlength is calculated to be 0.135/0.135 cm⁻¹, i.e. 1 cm. Similarly,if an (OD998−OD₉₁₀) value of 0.135 is determined, then the unknownoptical pathlength is 0.100/0.135 cm⁻¹, i.e. 0.741 cm. As anotherexample, optical pathlengths through substantially aqueous samples maybe determined from any measured (OD₉₉₈−OD₉₀₀) value by employing theconstant 0.137 cm⁻¹ (instead of 0.135 cm⁻¹) in a similar fashion. As athird example, optical pathlengths through substantially aqueous samplesmay be determined from any measured (OD₉₉₈−OD₁₀₉₀) value by employingthe constant 0.110 cm⁻¹ in a similar fashion. It will be recognized bythose skilled in the art of photometry that any constant so determinedfor any predetermined mixture of aqueous and nonaqueous solvents, may beused (together with measurement of the NIR absorbance properties of thepredetermined mixture) for determination of any unknown opticalpathlength for the mixture.

EXAMPLE 7 Elimination of Error in Determination of Optical Pathlengthdue to Variation in Solvent Composition

In this example, NIR absorption spectra, between 750 and 1100nanometers, were acquired as described in Example 6. The samples weremaintained near room temperature (at about 20 to 25° C.).

FIG. 7 shows the NIR absorption spectra of pure water, 0.1 M, 0.5 M ,and 1.0 M citric acid solutions (in water). The citric acid solutionsshow relatively insignificant deviation from the spectrum of water atthe lowest, 0.1 M concentration. The deviation however increases withincreasing concentration and is greatest at the highest (1.0 M) citrateconcentration.

FIG. 8 similarly shows the NIR absorption spectra, between 750 and 1100nanometers, of either pure water, 0.1 M, 0.5 M, or 1.0 M sucrosesolutions (in pure water). Similar to the citric acid solutions, thesucrose solutions show relatively insignificant deviation from thespectrum of pure water for the lowest, 0.1 M concentration. As forcitrate, however, the deviation increases with increasing soluteconcentration and is greatest at the highest (1.0 M) concentration. Thedeviation caused by sucrose is slightly more pronounced than that causedby citrate. The value of (OD₉₇₀−OD₉₁₀) is about 20% less for 1.0 Msucrose compared to pure water. Significantly better, the value ofeither (OD₉₉₈−OD₉₁₀) or (OD₉₉₈−OD₉₁₀) are only about 9% less for 1.0 Msucrose compared to pure water. While significant improvement indetermining optical pathlength is obtained by measuring absorption oflight in the “isosbestic wavelength region” near 998 nanometers,substantially complete elimination of error in such determinations, withall aqueous samples, however, is not possible.

EXAMPLE 8 Incorporation of a Reference Solvent Liquid of Known OpticalPathlength

In order to substantially eliminate errors in determination of unknownoptical pathlength of sample solutes dissolved at high concentration ina solvent liquid, an improved method with the following steps isemployed:

1. Place a reference comprising a reference sample solvent in a knownoptical pathlength, and a sample, comprising a sample in the samplesolvent, in an unknown optical pathlength, and

2. Measure:

a) a first optical density value (A_(REFλ1)) of the reference samplesolvent at a first preselected wavelength in the NIR where the sampleanalyte does not absorb light substantially and where absorption oflight by the sample solvent is near a local maximum (for example in theregion of 950 to 1000 nanometers for an aqueous solvent), and

b) a second optical density value (A_(REFλ2)) of the reference samplesolvent at a second preselected wavelength in the NIR where neither thesample analyte nor the reference sample solvent absorb lightsubstantially (for example in the region of 900 to 910 nanometers, orthe region from 1060 to 1080 nanometers, for an aqueous solvent), and

c) a third optical density value (A_(SMPλ1)) of the sample at the firstpreselected wavelength, and

d) a fourth optical density value (A_(SMPλ2)) of the sample at thesecond preselected wavelength, and

3. Calculate the optical pathlength as: $\begin{matrix}{{{Sample}\quad {Light}\quad {Absorption}\quad {Pathlength}} = \frac{{Reference}\quad {Light}\quad {Absorption}\quad {Pathlength}\quad \left( {A_{{SMP}\quad \lambda \quad 1} - A_{{SMP}\quad \lambda \quad 2}} \right)}{\left( {A_{{REF}\quad \lambda \quad 1} - A_{{REF}\quad \lambda \quad 2}} \right)}} & (12)\end{matrix}$

EXAMPLE 9 A Device Incorporating A Reference Solvent Liquid of KnownOptical Pathlength

Advantageously, a device will enclose both the reference and the sampleso that the temperature of the reference and the sample will besubstantially the same temperature, generally within a range of 2° C.and more generally with a range of 5° C. Also advantageously, the devicewill enclose a multiplicity of samples, e.g. an 8×12 array of samples ina 96-well multiassay plate, at a multiplicity of sample sites maintainedat substantially the same temperature as the reference. A preferredembodiment of the present invention is herein described. The device wasused in following method steps 1-3 and Equation 4 and 5 in Example 2.The device measures unknown optical pathlengths of a multiplicity ofassay sites with the aid of an incorporated reference liquid of knownoptical pathlength. In operation, a user performs the followingoperations:

(a.) The reference liquid is placed in a cuvette, of known opticalpathlength, within the device. The reference liquid is preselected to besimilar in solvent composition and temperature to the samples.(Optimally but not required, the sample analyte will be present in thereference liquid.)

(b.) Next, the samples on a multiassay plate, are placed in the deviceso that the samples and the reference liquid are maintained atsubstantially the same temperature (to within 1-2° C.).

(c.) The device measures the transmission of NIR light through each ofthe liquid samples and through the reference liquid of known opticalpathlength.

(d.) The device compares the transmission of light through both thesamples and the reference liquid and calculates the optical pathlengthof the samples.

Having determined the optical pathlength through each of the samples ina multi-assay plate, the device also may be used to determine theconcentration of analytes in such samples by determining the absorbanceof the analytes at a preselected wavelength. The results of suchdeterminations, therefore, may now be expressed in terms of opticaldensity per unit pathlength, e.g. A·cm⁻¹. Customarily the results willbe expressed in optical density per 1 cm pathlength. For example, if thesample material absorbs at 405 nanometers wavelength and the opticaldensity of the sample at 405 nanometers, A₄₀₅, if determined by thedevice to be 0.150 O.D. units; and the optical pathlength of the sample,determined by steps a-d above is determined to be 0.5 cm, then thecalculated A₄₀₅·cm⁻¹ value will be 0.300.

Once the optical pathlength is known, the concentration of analyte maybe determined by Beer-Lambert Law given in equation (1), from theextinction coefficient ε_(λ) at a preselected wavelength λ.

Shown in FIG. 9 is a photometric measuring system 10 for monitoring theoptical characteristics of a multiplicity of samples contained on amultiassay plate 12 having multiplicity of sample sites with variableoptical pathlength. The system has at least one reference site of knownoptical pathlength. The system 10 is comprised of a light source means22 which directs light to a wavelength selection means 23, which causesa substantially monochromatic band of light to pass into a lightdistribution means 24. The light distribution means 24 directs light to:

a) a means for retaining a reference optical pathlength of knownpathlength, shown in FIG. 9 as a cuvette means 40. Light transmittedthrough the reference optical pathlength is detected by a photodetectormeans 26, and

b) a chamber means 16 which encloses the multiplicity of sample sites.

The multi-assay plate 12 is carried by a plate carrier means 20 so as toposition the sample sites so that light directed by the lightdistribution means 24, and transmitted by the samples is detected by thephotodetector means 26. A temperature control means 28 controls thetemperature within the chamber means 16 and the cuvette means 40.

Electrical signals from the photodetector means 26 are sent to anacquisition and control processor means 14 which is in electricalcommunication with a central processor unit means 15. The centralprocessor means 15 may send data directly to a printer and be controlledby a user. Advantageously, however, the central processor means 15 willbe interfaced to a user interface computer 30, which enables the user tocontrol the system 10, acquire data, visualize data, compute dataparameters from the acquired data, and ultimately to export the data orparameters to an external printing device.

FIG. 10 is a detailed description of a preferred embodiment of thephotometric measuring system 10. Except for the disclosure given below,the preferred embodiment is identical to the preferred device disclosedin U.S. patent application Ser. No. 08/228,436 filed Apr. 15, 1994 whichis incorporated herein by reference. The system 10 produces a beam ofsubstantially monochromatic light, in the form of flashes, and deliversthis light sequentially to a plurality of light channels, eight in thepreferred embodiment, to sequentially illuminate the fluid sample in themultiassay plate 12.

An excitation light source 50, such as a xenon flash lamp, emits lightflashes containing wavelengths between at least 200 nanometers and 1100nanometers. Light from the excitation light source 50 beams through anaperture 51 limiting the light arc (61) to approximately ten degrees(10°). This light then passes through a source lens 52, which focusesthe light through one of a series of filters 55, included on a filterwheel 56, upon a monochrometer, generally designated 54. The excitationlight source 50, aperture 51, and source lens 52 cooperate to define thelights source means 22.

The source lens 52, in this preferred embodiment is a fused silicaplano-convex lens with a 12.7 millimeter diameter, a 16 millimeter focallength, and an optical magnification of 1×. The source lens 52 is spaced32 millimeters from the excitation light source 50 and 32 millimetersfrom the entrance slit 53 where light enters the monochrometer 54. Acollimating/focusing mirror 57 reflects and collimates the light beamonto a rotatable diffraction grating 59. There the light is dispersed atan angle with respect to the grating. This angle is dependent upon thewavelength of light striking the grating. The dispersed light falls backon the collimating/focusing mirror 57 which focuses substantiallymonochromatic light, within a narrow wavelength band, upon an exit slit63. Thus, the wavelength range (bandpass) of substantially monochromaticlight passing through exit slit 63 is dependent upon the wavelength oflight and the angle of the grating 59 with respect to the collimatedlight beam. The wavelength of maximal intensity of light passing throughthe exit slit may be preselected by rotating the grating 59 with respectto the incident light coming from mirror 57. The bandpass ofmonochromatic light passing through exit slit 63 is dependentprincipally upon the optical distance from grating 59 to exit slit 63,as well as the widths of exit slit 63, entrance slit 53 and aperture 51.

Exit slit 63 preferably, 0.7 in width and 1.3 millimeters in height, isformed by a metal end cap forming the end of a bundle of optical fibers58 which accepts the substantially monochromatic light. Cooperating todefine the wavelength selection means 23 are filter wheel 56, opticalfilters 55, and monochrometer 54. The output of monochromator 54provides light having a predetermined, continuously selectable, secondwavelength range within the first wavelength range provided by lightsource 50. In the preferred embodiment disclosed herein, the secondwavelength range has a predetermined bandpass width, defined as thewavelength width at one-half maximum light transmission, of about 2nanometers for all center-band wavelengths continuously selectable bythe user between 250 and 750 nanometers. The bandpass width may bepredetermined within a range of about 1 to 20 nanometers by changing thewidth of the exit slit 63, e.g. by employing a mechanically adjustableslit as the exit slit 63.

In the preferred embodiment optical fiber bundle 58 includes nineteen(19) optical fibers each 200 microns in diameter with a numericalaperture of 0.22, each arranged at the input in three (3) rows of six(6), seven (7), and six (6) fibers. This effectively defines a 0.7millimeter by 1.3 millimeter rectangular exit slit 63. The output of theoptical fiber 58 is configured as a circle with a diameter of 1.3millimeters. Light from the output of fiber 58, which is emitted over asolid angle of about ten degrees, is split by a beam splitter 60, asapphire window in this preferred embodiment. The beam splitter 60splits the light into a test light that passes through the beam splitter60 to a rotor assembly 70 and a reference light that reflects from thebeam splitter 60 to a flat reference mirror 62. The reference mirror 62reflects the reference light through a reference lens 66 to a referencephotodetector 64 of the photodetector means 26. The reference lens 66 isa bi-convex lens, is made of fused silica, has a focal length of 6.8millimeters, and has a diameter of 6.8 millimeters.

The intensity of light flashes emitted by the Xenon flash light 50 mayvary by as much a 50% between successive flashes due to variations inthe energy and position of the flash arc within the flash lamp. Thereference photodetector 64 outputs an electrical signal; representativeof the amplitude of the monochromatic light carried by the optical fiber58 for each flash of the light excitation source 50. This electricalsignal is used as an intensity reference for the reading of sample lighttransmitted through samples in the multi-assay plate 12.

The rotor assembly 70 includes two substantially identical rotor mirrors71 and 72 to redirect the light by 180° (degrees) (each mirror reflectslight by 90°) and a rotor lens 74 to focus the light beam between therotor mirrors 71 and 72. The rotor mirrors 71 and 72 and rotor lens 74act to reduce the spot size of the light beam from 1.3 millimeterdiameter at the input of the rotor assembly 70, which is the output ofthe optical fiber 58, to 0.65 millimeters at the output, which is theinput of a selected one of nine (9) receiving optical fibers 76 or theinput of a reference distribution optical fiber 90. The reduction inlight beam diameter within the rotor 70 allows substantially all of thelight to be launched at a solid angle of about 20° into the receivingfibers 76 of the light distribution means 24, greatly enhancingefficiency of sample light transmitted through the rotor 70. Care istaken so that the sample light is not focused in such a way that itexceeds the numerical aperture of the receiving optical fibers 76 and 90which will accept light over a solid angle of about 24°.

The optical distribution channels are defined by the receiving opticalfibers 76 and 90, made of solid silica or quartz, 1 millimeter indiameter, with a numerical aperture of 0.22. Light from the sampledistribution optical fibers 76 reflects off a sample light mirror 78,made of MgF₂ with a flat surface, into a substantially vertical samplelight distribution direction. A sample light aperture 80 further limitsthe numerical aperture of the light beam. A sample light lens 82 and asample light photodetector lens 86, each a biconvex lens made of fusedsilica with a 6.8 millimeter focal length and a 6.8 millimeter diameter,further focus the sample light. For ease of illustration, FIG. 10 showsonly one of a series of eight substantially identical sample lightdistribution optical fibers 76, sample light mirrors 78, sample lightapertures 80, sample light lenses 82 and sample light photodetectorlenses 86.

A reference pathlength distribution optical fiber 90 directs referencepathlength light from optical rotor 70 to reference pathlength lens 92,through a reference cuvette of known optical pathlength 94, which isretained in place by a cuvette holder 96. Customarily photometricmeasuring system 10 provides cuvette holder 96 without cuvette 94.During use of the invention, the user selects an appropriate referencecuvette which may be made of quartz, glass, polystyrene, polymethacylateor other suitable transparent material. Cuvette 94 and cuvette holder 96cooperate to define cuvette means 40. Reference pathlength lighttransmitted through cuvette 94 is detected by reference pathlengthphotodetector 98.

In operation, first a reference sample solvent is placed in thereference cuvette of known optical pathlength (e.g. a 1.00 cm opticalpathlength) and samples in the sample solvent are placed in one, ormore, wells of the multi-assay plate 12. The multi-assay plate is thenplaced on a plate carrier means 20 within chamber means 16. The userinstructs the system 10 to “read” one-or-more preselected samples. Theplate carrier means positions the preselected samples between the samplelight lenses 82 and sample light photodetector lenses 86 so that lightfrom the sample distribution optical fibers 76 will pass substantiallyvertically through the samples without striking the side-walls of themulti-assay plate, which contains the samples.

In a reading cycle the rotor assembly 70 first rotates so as todistribute light to a dark channel, so that no light falls upon samplephotodetectors 88 or pathlength reference photodetector 98 when lightsource 50 emits a flash of light. Electrical signals from samplephotodetectors 88 and pathlength reference photodetector 98 provide azero light baseline value for each photodetector when the light isdistributed to a dark channel. The rotor assembly 70 secondly rotates soas to distribute reference pathlength light through the referencecuvette 94, which contains reference sample solvent in a known opticalpathlength. The reference cuvette is retained in place by a cuvetteholder 96. Reference pathlength light transmitted through cuvette 94 isdetected by reference pathlength photodetector 98 which, in turn, sendsan electrical signal related to the intensity of detected light toacquisition and control processor means 14.

The rotor assembly 70 next rotates to sequentially illuminate the seriesof eight sample light distribution optical fibers 76 so as tosequentially illuminate the fluid samples in the multiassay plate 12.The multiplicity of samples receives sample light having a substantiallyidentical spectral distribution of light intensity provided bymonochrometer 54. The photometric device 10 described provides the abovesample light characteristics to a multiplicity of samples in amulti-assay plate within short periods of times so that the opticalproperties of 96 samples contained in a conventional 8×12 microplate maybe determined within approximately 9 seconds (generally from 8 to 10seconds). Determination of optical pathlength requires measurement at,at least 2 different wavelengths, λ1 and λ2. Thus, in order to measureoptical pathlength through the samples the measurement procedure isfirst performed at λ1 and then repeated at λ2, thus the measurements iscompleted within 18 seconds (generally from 16 to 20 seconds).Optionally, the reading process may be adjusted to proceed at a slowerpace (for example over 10 minutes or more) when there is no need forrapid determinations.

EXAMPLE 10 Elimination of Error in Determination of Absorbance ofSamples per Unit Optical Pathlength

The device disclosed in Example 9 may be used to substantially eliminateerror in the determination of the ratio of absorbance of analytes withinliquid samples and the optical pathlength. These ratiometricmeasurements are given as “Light Absorbance per Unit Pathlength” inExamples 2 and 3 above.

In order to perform such ratiometric measurements, the deviceadditionally monitors the absorbance of an analyte, in the one or moresamples sequentially, at a preselected wavelength. This value is givenas “Sample A_(x),” in examples 2 and 3 above. The device then computesthe ratio of Sample A_(x), and the optical pathlength, for each sample,to give “Light Absorbance per Unit Pathlength”.

The examples below show further methods resulting in improved precisionin determination of light absorbance by an analyte dissolved in asolvent by using vertical-beam photometry.

EXAMPLE 11 Methods for Improving Precision of Optical PathlengthDetermination in a Vertical-Beam Photometer

1. Evaluation of precision was carried out with SPECTRAmax®PLUSmicroplate spectrophotometer. For these evaluations 200 μl of 0.05 Mpotassium phosphate buffer, adjusted to pH 7.00 with NaOH (andcontaining yellow food coloring as the test analyte) was dispensed inthe wells of a quartz, 96-well microplate (available from MolecularDevices as Part Number R8024). The test analyte solution is availablefrom Fisher Scientific as Catalog Number SB107-500 (pH 7.00 BufferSolution).

The test analyte solution has a broad spectral absorption maximumbetween 420 and 440 nanometers which returns close to a baseline valuebetween 510 to 520 nanometers. The wavelength for determining analyteabsorbance was selected to be 420 nanometers near the absorptionmaximum. Precision absorbance studies were performed in 96 replicatewells of the quartz microplate. The test analyte was dispensed into themicroplate wells and analyte absorbance per unit solvent pathlength wasmeasured in each well. Two method variables were evaluated in all fourpossible combinations for effect on measurement precision. The firstvariable was to determine the absorbance of the analyte at a singlewavelength (A₄₂₀) (single wavelength mode) or at dual wavelengths(A₄₂₀−A₅₂₀) (dual wavelength mode). In the dual wavelength mode, thesecond absorbance value (A₅₂₀) is used as a reference absorbancemeasurement. In all cases, absorbance of the solvent was measured at twowavelengths (1000 and 900 nanometers) in order to determine opticalpathlength of the solvent. Thus, at least three absorbance values arealways determined at at least three different wavelengths. LightAbsorbance per Unit Pathlength is then calculated as:0.1433(A₄₂₀)/(A₁₀₀₀−A₉₀₀) or alternatively0.1433(A₄₂₀−A₅₂₀)/(A₁₀₀₀−A₉₀₀).

In practice, the absorbance of each sample in the multi-assay plate (inthis case a 96-well microplate) was measured at 420, 520, 900 and 1000nanometers. A second method variable was to (A) measure all absorbancesvalues in each individual sample at all preselected (in this case threeor four) wavelengths without moving the samples (a “Stationary Read”).This was accomplished, in this example, by selecting 420, 520, 900 and1000 nanometers bandpass light, sequentially, with monochrometer 54 foreach sample before moving the microplate 12 with plate carrier means 20.Alternatively, other methods of spectral scanning without samplemovement, such as emplying a diode-array detector together with aspectral dispersion means such as a prism, grating, tunable opticalfillers, array of optical fillers, etc., may be used. In the alternative(B) of the second method variable, absorbance values are measured on allsamples at a first wavelength (by moving the samples), switching to asecond wavelength by adjusting the monochrometer and measuringabsorbances values on all samples at the second wavelength (again bymoving the samples), and repeating the process until all absorbancevalues, at all selected wavelength values, have been determined. In bothcases repositioning of the multi-assay is performed by the motorizedplate carrier which centrally positions the sample wells under the lightpaths of the fiber optic channels.

Table IV gives the results of a precision test using the fourcombinations of the two method variables. Dual wavelength absorbancemeasurements gave greater precision (less error) than single wavelengthabsorbance measurements. Also, absorbance measurements using multiplewavelengths gave the greatest precision when measurements were made atall the wavelengths prior to moving the fluid samples (“StationaryRead”). The lowest error was observed when dual wavelength absorbanceswere carried out in combination with a Stationary Read. In that case,the standard deviation of Absorbance/cm Pathlength measurements was0.003 absorbance units per cm (coefficient of variation=0.8%). Incontrast when single wavelength absorbance measurements were made andthe samples were not stationary, the standard deviation of Absorbance/cmPathlength measurements was 0.008 absorbance units per cm (coefficientof variation=2.1%).

TABLE IV Error in Determination of Analyte Absorbance per Unit OpticalPathlength Stationary Non Stationary A₄₂₀-A₅₂₀ *0.003 *0.006 A₄₂₀ *0.006*0.008 *Standard Deviation (Absorbance units/cm optical pathlength) formeasurement of a single well. Data taken with 200 μl sample volumes in aquartz 96 well microplate in a SPECTRAmax ® Plus microplatespectrophotometer. N = 96. Mean pathlength = 0.522 cm. Mean A₄₂₀ and(A₄₂₀-A₅₂₀) per cm pathlength = 0.380.

The difference in absorbance at 1000 and 900 nanometers was used tocompute the optical pathlength through the aqueous test analytesolution. As shown in FIGS. 5 and 6, the absorbance of solvent in diluteaqueous solutions of analytes is substantially independent oftemperature within 20 nanometers of the temperature isosbesticwavelength near 1000 nanometers; within 40 nanometers of anothertemperature isosbestic wavelength near 1110 nanometers; and in theregion of 750 to 940 nanometers encompassing the temperature isosbesticwavelength near 920 nanometers. The difference in absorbance between anytwo temperature isosbestic wavelength regions may be utilized formonitoring the pathlength of the solvent. The temperature isosbesticpoints near 1000 and 920 nanometers were selected to determine theoptical pathlength through the aqueous test analyte solution because thedifference in absorbance for any given optical pathlength is greatestwith these two wavelengths, yet these two wavelength values allrelatively close, one to another. Further, it is advantageous to selectthe wavelengths to be as long as possible to a) minimize possibleinterference from substances which absorb strongly in the visiblewavelengths and b) minimize interferences from light scatteringphenomena (e.g. Raleigh Scattering, which is inversely proportional towavelength raised to the fourth power).

As a consequence of selecting a temperature isosbestic wavelength andnot wavelength at an absorbance maximum or minimum, the slope of changein absorbance with change in wavelength is quite large. Wavelengthselection precision, thus is very important for reproducibly andaccurately measuring optical pathlength. Further accuracy is realizedwhen all channels of a multi-channel vertical-beam photometer areexactly matched, or alternatively, separately calibrated. The followingexample shows that additional precision may be obtained by separatelycalibrating each channel of a multiple-(8) channel microplatespectrophotometer.

2. Separate calibration of each optical channel of a vertical-beamphotometer may be performed by placing a cuvette of constant opticalpathlength in each channel the sample compartment of a vertical-beamphotometer and separately measuring the differential absorbance ofsample solvent (in this case water) in each channel. For example(A₁₀₀₀−A₉₀₀) may be measured for water in a 1 cm pathlength cuvette. Thedifferential absorbance values measured respectively for each opticalchannel are stored and subsequently recalled to calculate opticalpathlength from differential absorbance values measured on aqueoussamples of unknown optical pathlength.

Alternatively, separate calibration of each optical channel may beperformed by employing a horizontal-beam reference cuvette (as shown inFIG. 10) and measuring the absorbance of an analyte dissolved in areference solution which is contained in the reference cuvette. (This iscalled the reference analyte calibration method.) In this measurement,absorbance by the cuvette containing a reference solvent (without thereference analyte) is subtracted from the absorbance value taken withthe reference analyte dissolved in the reference solvent to obtain acalibration absorbance value for the reference analyte. Next, the samereference solution is placed into the sample wells of a multi-assayplate in a housing enclosing the multi-assay plate in the optical pathof the vertical-beam photometer. Again, absorbance of the multi-assayplate containing a reference solvent (without the reference analyte) issubtracted from the absorbance values taken with the reference analytedissolved in the reference solvent to obtain a calibration absorbancevalue for the reference analyte in the multi-assay plate. In addition,differential absorbance of the sample solvent is measured in eachchannel. For example, (A₁₀₀₀−A₉₀₀) may be measured when the samplesolvent is water. This measurement is repeated with the same referencesolution for each optical channel of the vertical-beam photometer. Fromthe results of reference analyte absorbance and differential absorbanceof the sample solvent in each channel, a calibration value is calculatedfor each optical channel so that the absorbance of the analyte per unitoptical pathlength for each vertical-beam photometer channel isidentical to the result obtained in the reference cuvette.

The reference analyte calibration method described above was applied toeach channel of a SPECTRAmax®PLUS microplate spectrophotometer. Nexterror analysis for determination of Analyte Absorbance per Unit OpticalPathlength was determined for the same analyte, under similar conditionsas were used to generate the data shown in Table IV. Analyte absorbancewas measured as (A₄₂₀−A₅₂₀) under conditions giving optimal precision.When an average calibration value was used for all 8 channels of thevertical-beam photometer a standard deviation of 0.0021 (0.55%coefficient of variation) was observed. When eight (8)separately-determined calibration values were used for the respective 8channels of the SPECTRAmax®PLUS microplate spectrophotometer, a standarddeviation of 0.0011 (0.29% coefficient of variation) was observed. Ineach case, the results were the mean of 3 multi-assay plates, eachcontaining 96 samples (N=288). Thus, measurement precision wasapproximately doubled by employing solvent pathlength calibration valuesindividually determined for each optical channel.

EXAMPLE 12 Measurement of Solvent Absorbance at NIR Wavelengths Greaterthan 1100 Nanometers.

In vertical-beam photometry, optical pathlengths generally vary fromabout 0.05 cm to about 2.0 cm. Most frequently the sample volumes arebetween 2 millimeters and 1.0 cm. For precise analysis of AnalyteAbsorbance per Unit Optical Pathlength on very small sample volumes,precise measurement of Optical Pathlength on short pathlengths between0.05 cm and 0.5 cm is advantageous. As shown in FIGS. 5-8, thedifferential absorbance of aqueous solutions, at any two wavelengthsbetween 750 nanometers and 1100 nanometers is less than 0.2 for a 1 cmpathlength. For a 0.1 cm pathlength, for example, this results in adifferential absorbance less than 0.020. The precision of individualabsorbance measurements in vertical-beam photometers is generally about0.001 absorbance units. Thus, significant error (in this case about 7%coefficient of variation) will be inherent in measurement of 0.1 cmoptical pathlengths in aqueous solutions. Increasing the amplitude ofabsorption of the solvent, or alternatively, increasing the precision ofabsorbance measurements is necessary to improve analytical precision.

The amplitude of the absorbance of solvents generally employed inanalytical chemistry, such as alcohols, ketones, aromatic hydrocarbons(e.g. benzenes, toluenes and anilines), alkanes, furans, sulfoxides, aswell as aqueous media, are generally quite small in the region between770 nanometers and 1100 nanometers. The amplitude of absorbance of thesesolvents increases at wavelengths longer than 1100 nanometers. Thesewavelengths generally will be within the near infrared region (750-2500nm wavelength) or the infrared region of the electromagnetic spectrum(2.5 micron to 1000 micron wavelength).

Analyte Absorbance, Optical Pathlength and Analyte Absorbance per UnitOptical Pathlength of three different analytes (at three differentanalyte analysis wavelengths) were determined by vertical-beamphotometry. In each case, optical pathlength by measuring lightabsorption by a sample solvent is determined both at temperatureisosbestic wavelengths less than 1100 nanometers and at temperatureisosbestic wavelengths greater than 1100 nanometers. For wavelengthsless than 1100 nm, differential absorbance of water at the temperatureisosbestic wavelengths of 900 and 1000 nanometers preferably is used todetermine solvent pathlength (as described above). For wavelengthsgreater than 1100 nm, differential absorbance of water at thetemperature isosbestic wavelengths of 1100 and 1200 nanometerspreferably is used to determine solvent pathlength. For absorbancemeasurements employing wavelengths longer than 1100 nanometers, thesilicon photodetectors (both the reference and sample measurementsilicon photodiodes) in one optical channel of a SPECTRAmax®PLUSvertical-beam spectrophotometer (1 sample and 1 reference photodetector)were replaced with InGaAs PIN Photodiodes (Type No. G5832-03, obtainedfrom Hamamatsu Corporation, Hamamatsu City, Japan). For comparisonpurposes, the absorbance of each analyte also was measured in a 1 cmfixed optical pathlength cuvette by horizontal-beam photometry.

The results of the absorbance measurements are summarized in TABLE V.Vertical-beam photometry in each case was performed at 6 differentoptical pathlengths. The first analyte listed is bovine serum albumin(BSA) at 2 mg/ml in phosphate-buffered saline (0.05 M sodium phosphate,0.1M NaCl, pH 7.2 (PBS)). Absorbance of the BSA analyte was determinedat 280 nm. When analyzed in the 1 cm fixed optical pathlength cuvette,A₂₈₀ was 0.995. When analyzed by vertical-beam photometry employing 900nm and 1000 nm differential absorbance to determine optical pathlengthof the PBS solvent, A₂₈₀ (per cm optical pathlength) ranged from 1.033,at 350 μl sample volume, to 1.054 at 100 μl sample volume. The latervalue is 5.9% greater than the 0.995 A₂₈₀ reference value determined inthe 1.0 cm fixed pathlength cuvette. In contrast, when analyzed byvertical-beam photometry employing 1200 nm and 1100 nm differentialabsorbance to determine optical pathlength of the PBS solvent, A₂₈₀ (percm optical pathlength) ranged from 1.007, at 350 μl sample volume, to1.017 at 100 μl sample volume. The later value is only 2.2% greater thanthe 0.995 A₂₈₀ reference value. Thus, the accuracy at the 100 μl samplevolume was substantially improved by employing 1200 nm and 1100 nmdifferential absorbance to determine optical pathlength of the PBSsolvent.

The second analyte shown in TABLE V was yellow food coloring in 0.05 Mpotassium phosphate buffer, adjusted to pH 7.00 with NaOH. The testanalyte solution is available from Fisher Scientific as Catalog NumberSB107-500 (pH 7.00 Buffer Solution). Absorbance of the yellow foodcoloring analyte was determined at 420 nm. When analyzed in the 1 cmfixed optical pathlength cuvette, A₄₂₀ was 0.389. When analyzed byvertical-beam photometry employing 900 nm and 1000 nm differentialabsorbance to determine optical pathlength of the PBS solvent, A₄₂₀ (percm optical pathlength) ranged from 0.395 at 350 μl sample volume, to0.403 at 100 μl sample volume. The later value is 4.0% greater than the0.389 A₄₂₀ reference value determined in the 1.0 cm fixed pathlengthcuvette. In contrast, when analyzed by vertical-beam photometryemploying 1200 nm and 1100 nm differential absorbance to determineoptical pathlength of the 0.05 M potassium phosphate buffer solvent,A₄₂₀ (per cm optical pathlength) ranged from 0.384, at 350 μl samplevolume, to 0.385 at 100 μl sample volume. The later value is only about0.3% less than the 0.389 A₄₂₀ reference value. Thus, the accuracy at the100 μl sample volume again is greatly improved by employing 1200 nm and1100 nm differential absorbance to determine optical pathlength of thePBS solvent.

The third analyte shown in TABLE V was Napthol Green B dye (AldrichChemical Co., Milwaukee, Wis.) dissolved in water (50 μg/ml). Absorbanceof the Napthol Green B dye analyte was determined at 720 nm. Whenanalysed in the 1 cm fixed optical pathlength cuvette, A₇₂₀ was 0.569.When analysed by vertical-beam photometry employing 900 nm and 1000 nmdifferential absorbance to determine optical pathlength of the PBSsolvent, A₇₂₀ (per cm optical pathlength) ranged from 0.917 at 350 μlsample volume, to 0.904 at 100 μl sample volume. All of these values areapproximately 60% greater than the 0.569 A₇₂₀ reference value determinedin the 1.0 cm fixed pathlength cuvette. This very large error isattributed to significant differential absorbance of the Napthol Green Bdye at 900 and 1000 nanometers. In contrast, when analysed byvertical-beam photometry employing 1200 nm and 1100 nm differentialabsorbance to determine optical pathlength of the water solvent, A₇₂₀(per cm optical pathlength) ranged from 0.569, at 350 μl sample volume,to 0.560 at 100 μl sample volume. The later value is about 1.6.% lessthan the 0.569 A₇₂₀ reference value. Thus, the accuracy at the 100 μlsample volume again is greatly improved by employing 1200 nm and 1100 nmdifferential absorbance to determine optical pathlength of the (aqueous)solvent. The considerable interference of the Napthol Green B dye isremoved by performing the optical pathlength determination at the 1100and 1200 temperature isosbestic wavelengths of the (aqueous) solvent. Ingeneral, employing absorbance measurements at temperature isosbesticwavelengths greater than 1000 nanometers to determine optical pathlengthwill provide considerable increased accuracy.

TABLE V Absorbance/(Cm Optical Pathlength) With Optical PathlengthMeasured at Different NIR Wavelengths in Aqueous Samples AbsorbanceSolvent Pathlength Sample Volume in Microplate 1 cm Sample/WavelengthWavelengths 350 μL 300 μL 250 μL 200 μL 150 μL 100 μL Cuvette BSA, 2mg/ml 1200/1100 nm 1.007 1.019 1.032 1.021 1.026 1.017 0.995 A_(280 nm)1000/900 nm  1.033 1.030 1.030 1.033 1.044 1.054 Fisher pH 7.0 1200/1100nm 0.384 0.386 0.386 0.385 0.385 0.385 0.389 (yellow) Buffer 1000/900nm  0.395 0.396 0.398 0.398 0.396 0.403 A_(420 nm) Napthol Green B,1200/1100 nm 0.569 0.571 0.577 0.566 0.573 0.560 0.569 50 ug/ml 1000/900nm  0.917 0.913 0.914 0.915 0.916 0.904 A_(720 nm)

From the foregoing it will be appreciated that, although specificembodiments of the invention have been described herein for purposes ofillustration, various modifications may be made without deviating fromthe spirit and scope of the invention.

What is claimed is:
 1. A photometric method for measuring lightabsorption pathlengths of samples of analyte dissolved in water whereinthe samples are in wells of a multi-assay plate and where there is aninterface between the samples and air comprising determining the samplelight absorption pathlength for each of the samples in the wells of themultiassay plate in accordance with the formula:${{Sample}\quad {light}\quad {absorption}\quad {pathlength}} = {{Reference}\quad {light}\quad {absorption}\quad {pathlength} \times \frac{\left( {{A\quad {smp}\quad {\lambda 1}} - {{Amp}\quad {\lambda 2}}} \right)}{\left( {{A\quad {ref}\quad {\lambda 1}} - {A\quad {ref}\quad {\lambda 2}}} \right)}}$

wherein (A smp λ₁−A smp λ₂) is the difference in absorptions of light ofwavelength λ₁ and λ₂ between 700 nanometers and 2500 nanometers which ispassed vertically through the samples and to the interface between thesamples and air wherein (A ref λ₁−A ref λ₂) is the difference inabsorption of light of λ₁ and λ₂ passed through a known reference lightabsorption pathlength.
 2. The method of claim 1 wherein the value:$\frac{{reference}\quad {light}\quad {absorption}\quad {pathlength}}{{A\quad {ref}\quad \lambda_{1}} - {A\quad {ref}\quad \lambda_{2}}}$

is a predetermined number.
 3. The method of claim 1 wherein λ₁ and λ₂are isosbestic wavelengths between 700 nanometers and 2500 nanometers.4. The method of claim 3 wherein one of the wavelength between 988 and1008 nanometers and the other wavelength is between 1050 and 1150nanometers.
 5. The method of claim 3 wherein one of the wavelengths isbetween 998 and 1008 and the other wavelength is between 750 and 930nanometers.